Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [210,2,Mod(101,210)]
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, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("210.101");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 210.r (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: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 4 x^{11} + 11 x^{10} - 32 x^{9} + 64 x^{8} - 120 x^{7} + 237 x^{6} - 360 x^{5} + 576 x^{4} + \cdots + 729 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 131.4 | ||
Root | \(-0.111613 - 1.72845i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 210.131 |
Dual form | 210.2.r.b.101.4 |
$q$-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 \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(71\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.866025 | + | 0.500000i | 0.612372 | + | 0.353553i | ||||
\(3\) | −0.960885 | + | 1.44108i | −0.554767 | + | 0.832006i | ||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | −0.500000 | + | 0.866025i | −0.223607 | + | 0.387298i | ||||
\(6\) | −1.55269 | + | 0.767566i | −0.633883 | + | 0.313358i | ||||
\(7\) | −1.91871 | + | 1.82168i | −0.725206 | + | 0.688532i | ||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | −1.15340 | − | 2.76942i | −0.384467 | − | 0.923139i | ||||
\(10\) | −0.866025 | + | 0.500000i | −0.273861 | + | 0.158114i | ||||
\(11\) | 1.99775 | − | 1.15340i | 0.602344 | − | 0.347763i | −0.167619 | − | 0.985852i | \(-0.553608\pi\) |
0.769963 | + | 0.638089i | \(0.220275\pi\) | |||||||
\(12\) | −1.72845 | − | 0.111613i | −0.498961 | − | 0.0322198i | ||||
\(13\) | 5.00084i | 1.38698i | 0.720464 | + | 0.693492i | \(0.243929\pi\) | ||||
−0.720464 | + | 0.693492i | \(0.756071\pi\) | |||||||
\(14\) | −2.57250 | + | 0.618268i | −0.687529 | + | 0.165239i | ||||
\(15\) | −0.767566 | − | 1.55269i | −0.198185 | − | 0.400903i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −3.15115 | − | 5.45795i | −0.764266 | − | 1.32375i | −0.940634 | − | 0.339423i | \(-0.889768\pi\) |
0.176368 | − | 0.984324i | \(-0.443565\pi\) | |||||||
\(18\) | 0.385834 | − | 2.97509i | 0.0909420 | − | 0.701234i | ||||
\(19\) | 6.54470 | + | 3.77859i | 1.50146 | + | 0.866867i | 0.999999 | + | 0.00168616i | \(0.000536721\pi\) |
0.501460 | + | 0.865181i | \(0.332797\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | −0.781523 | − | 4.51544i | −0.170542 | − | 0.985350i | ||||
\(22\) | 2.30680 | 0.491812 | ||||||||
\(23\) | 5.51880 | + | 3.18628i | 1.15075 | + | 0.664385i | 0.949070 | − | 0.315066i | \(-0.102027\pi\) |
0.201679 | + | 0.979452i | \(0.435360\pi\) | |||||||
\(24\) | −1.44108 | − | 0.960885i | −0.294158 | − | 0.196140i | ||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | −2.50042 | + | 4.33086i | −0.490373 | + | 0.849351i | ||||
\(27\) | 5.09922 | + | 0.998953i | 0.981346 | + | 0.192249i | ||||
\(28\) | −2.53698 | − | 0.750813i | −0.479445 | − | 0.141890i | ||||
\(29\) | − | 3.83533i | − | 0.712204i | −0.934447 | − | 0.356102i | \(-0.884106\pi\) | ||
0.934447 | − | 0.356102i | \(-0.115894\pi\) | |||||||
\(30\) | 0.111613 | − | 1.72845i | 0.0203776 | − | 0.315571i | ||||
\(31\) | −3.79452 | + | 2.19077i | −0.681516 | + | 0.393473i | −0.800426 | − | 0.599432i | \(-0.795393\pi\) |
0.118910 | + | 0.992905i | \(0.462060\pi\) | |||||||
\(32\) | −0.866025 | + | 0.500000i | −0.153093 | + | 0.0883883i | ||||
\(33\) | −0.257468 | + | 3.98719i | −0.0448195 | + | 0.694081i | ||||
\(34\) | − | 6.30230i | − | 1.08083i | ||||||
\(35\) | −0.618268 | − | 2.57250i | −0.104506 | − | 0.434831i | ||||
\(36\) | 1.82168 | − | 2.38358i | 0.303614 | − | 0.397264i | ||||
\(37\) | 3.45465 | − | 5.98363i | 0.567941 | − | 0.983703i | −0.428828 | − | 0.903386i | \(-0.641074\pi\) |
0.996769 | − | 0.0803166i | \(-0.0255931\pi\) | |||||||
\(38\) | 3.77859 | + | 6.54470i | 0.612968 | + | 1.06169i | ||||
\(39\) | −7.20659 | − | 4.80523i | −1.15398 | − | 0.769453i | ||||
\(40\) | −0.866025 | − | 0.500000i | −0.136931 | − | 0.0790569i | ||||
\(41\) | 9.79371 | 1.52952 | 0.764760 | − | 0.644315i | \(-0.222857\pi\) | ||||
0.764760 | + | 0.644315i | \(0.222857\pi\) | |||||||
\(42\) | 1.58090 | − | 4.30125i | 0.243939 | − | 0.663697i | ||||
\(43\) | 2.55278 | 0.389296 | 0.194648 | − | 0.980873i | \(-0.437644\pi\) | ||||
0.194648 | + | 0.980873i | \(0.437644\pi\) | |||||||
\(44\) | 1.99775 | + | 1.15340i | 0.301172 | + | 0.173882i | ||||
\(45\) | 2.97509 | + | 0.385834i | 0.443500 | + | 0.0575168i | ||||
\(46\) | 3.18628 | + | 5.51880i | 0.469791 | + | 0.813703i | ||||
\(47\) | −0.828416 | + | 1.43486i | −0.120837 | + | 0.209296i | −0.920098 | − | 0.391688i | \(-0.871891\pi\) |
0.799261 | + | 0.600984i | \(0.205224\pi\) | |||||||
\(48\) | −0.767566 | − | 1.55269i | −0.110789 | − | 0.224111i | ||||
\(49\) | 0.362928 | − | 6.99059i | 0.0518469 | − | 0.998655i | ||||
\(50\) | − | 1.00000i | − | 0.141421i | ||||||
\(51\) | 10.8932 | + | 0.703417i | 1.52535 | + | 0.0984980i | ||||
\(52\) | −4.33086 | + | 2.50042i | −0.600582 | + | 0.346746i | ||||
\(53\) | −2.81699 | + | 1.62639i | −0.386944 | + | 0.223402i | −0.680835 | − | 0.732437i | \(-0.738383\pi\) |
0.293891 | + | 0.955839i | \(0.405050\pi\) | |||||||
\(54\) | 3.91658 | + | 3.41473i | 0.532979 | + | 0.464686i | ||||
\(55\) | 2.30680i | 0.311049i | ||||||||
\(56\) | −1.82168 | − | 1.91871i | −0.243433 | − | 0.256399i | ||||
\(57\) | −11.7339 | + | 5.80063i | −1.55420 | + | 0.768312i | ||||
\(58\) | 1.91767 | − | 3.32150i | 0.251802 | − | 0.436134i | ||||
\(59\) | −4.96573 | − | 8.60089i | −0.646483 | − | 1.11974i | −0.983957 | − | 0.178406i | \(-0.942906\pi\) |
0.337474 | − | 0.941335i | \(-0.390427\pi\) | |||||||
\(60\) | 0.960885 | − | 1.44108i | 0.124050 | − | 0.186042i | ||||
\(61\) | −5.18202 | − | 2.99184i | −0.663489 | − | 0.383066i | 0.130116 | − | 0.991499i | \(-0.458465\pi\) |
−0.793605 | + | 0.608433i | \(0.791798\pi\) | |||||||
\(62\) | −4.38153 | −0.556455 | ||||||||
\(63\) | 7.25805 | + | 3.21259i | 0.914428 | + | 0.404748i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −4.33086 | − | 2.50042i | −0.537176 | − | 0.310139i | ||||
\(66\) | −2.21657 | + | 3.32428i | −0.272841 | + | 0.409190i | ||||
\(67\) | 1.38358 | + | 2.39643i | 0.169031 | + | 0.292771i | 0.938080 | − | 0.346420i | \(-0.112603\pi\) |
−0.769048 | + | 0.639191i | \(0.779269\pi\) | |||||||
\(68\) | 3.15115 | − | 5.45795i | 0.382133 | − | 0.661874i | ||||
\(69\) | −9.89460 | + | 4.89136i | −1.19117 | + | 0.588851i | ||||
\(70\) | 0.750813 | − | 2.53698i | 0.0897393 | − | 0.303227i | ||||
\(71\) | 2.85910i | 0.339312i | 0.985503 | + | 0.169656i | \(0.0542657\pi\) | ||||
−0.985503 | + | 0.169656i | \(0.945734\pi\) | |||||||
\(72\) | 2.76942 | − | 1.15340i | 0.326379 | − | 0.135930i | ||||
\(73\) | −3.18851 | + | 1.84089i | −0.373187 | + | 0.215459i | −0.674850 | − | 0.737955i | \(-0.735792\pi\) |
0.301663 | + | 0.953415i | \(0.402458\pi\) | |||||||
\(74\) | 5.98363 | − | 3.45465i | 0.695583 | − | 0.401595i | ||||
\(75\) | 1.72845 | + | 0.111613i | 0.199584 | + | 0.0128879i | ||||
\(76\) | 7.55717i | 0.866867i | ||||||||
\(77\) | −1.73198 | + | 5.85231i | −0.197377 | + | 0.666933i | ||||
\(78\) | −3.83848 | − | 7.76475i | −0.434622 | − | 0.879185i | ||||
\(79\) | −1.27945 | + | 2.21607i | −0.143949 | + | 0.249327i | −0.928980 | − | 0.370129i | \(-0.879313\pi\) |
0.785031 | + | 0.619456i | \(0.212647\pi\) | |||||||
\(80\) | −0.500000 | − | 0.866025i | −0.0559017 | − | 0.0968246i | ||||
\(81\) | −6.33934 | + | 6.38849i | −0.704371 | + | 0.709832i | ||||
\(82\) | 8.48160 | + | 4.89686i | 0.936636 | + | 0.540767i | ||||
\(83\) | −1.83743 | −0.201684 | −0.100842 | − | 0.994902i | \(-0.532154\pi\) | ||||
−0.100842 | + | 0.994902i | \(0.532154\pi\) | |||||||
\(84\) | 3.51973 | − | 2.93454i | 0.384034 | − | 0.320185i | ||||
\(85\) | 6.30230 | 0.683580 | ||||||||
\(86\) | 2.21077 | + | 1.27639i | 0.238394 | + | 0.137637i | ||||
\(87\) | 5.52701 | + | 3.68532i | 0.592558 | + | 0.395107i | ||||
\(88\) | 1.15340 | + | 1.99775i | 0.122953 | + | 0.212961i | ||||
\(89\) | −2.94387 | + | 5.09894i | −0.312050 | + | 0.540486i | −0.978806 | − | 0.204790i | \(-0.934349\pi\) |
0.666756 | + | 0.745276i | \(0.267682\pi\) | |||||||
\(90\) | 2.38358 | + | 1.82168i | 0.251252 | + | 0.192022i | ||||
\(91\) | −9.10996 | − | 9.59518i | −0.954983 | − | 1.00585i | ||||
\(92\) | 6.37256i | 0.664385i | ||||||||
\(93\) | 0.489035 | − | 7.57326i | 0.0507105 | − | 0.785311i | ||||
\(94\) | −1.43486 | + | 0.828416i | −0.147994 | + | 0.0854446i | ||||
\(95\) | −6.54470 | + | 3.77859i | −0.671472 | + | 0.387675i | ||||
\(96\) | 0.111613 | − | 1.72845i | 0.0113914 | − | 0.176409i | ||||
\(97\) | − | 4.61723i | − | 0.468808i | −0.972139 | − | 0.234404i | \(-0.924686\pi\) | ||
0.972139 | − | 0.234404i | \(-0.0753139\pi\) | |||||||
\(98\) | 3.80960 | − | 5.87256i | 0.384827 | − | 0.593218i | ||||
\(99\) | −5.49845 | − | 4.20226i | −0.552615 | − | 0.422343i | ||||
\(100\) | 0.500000 | − | 0.866025i | 0.0500000 | − | 0.0866025i | ||||
\(101\) | −5.65702 | − | 9.79825i | −0.562894 | − | 0.974962i | −0.997242 | − | 0.0742165i | \(-0.976354\pi\) |
0.434348 | − | 0.900745i | \(-0.356979\pi\) | |||||||
\(102\) | 9.08209 | + | 6.05578i | 0.899261 | + | 0.599612i | ||||
\(103\) | 6.37747 | + | 3.68203i | 0.628391 | + | 0.362802i | 0.780129 | − | 0.625619i | \(-0.215154\pi\) |
−0.151738 | + | 0.988421i | \(0.548487\pi\) | |||||||
\(104\) | −5.00084 | −0.490373 | ||||||||
\(105\) | 4.30125 | + | 1.58090i | 0.419759 | + | 0.154280i | ||||
\(106\) | −3.25278 | −0.315938 | ||||||||
\(107\) | −7.29084 | − | 4.20937i | −0.704832 | − | 0.406935i | 0.104312 | − | 0.994545i | \(-0.466736\pi\) |
−0.809145 | + | 0.587609i | \(0.800069\pi\) | |||||||
\(108\) | 1.68449 | + | 4.91553i | 0.162090 | + | 0.472998i | ||||
\(109\) | 3.33156 | + | 5.77043i | 0.319105 | + | 0.552707i | 0.980302 | − | 0.197506i | \(-0.0632843\pi\) |
−0.661196 | + | 0.750213i | \(0.729951\pi\) | |||||||
\(110\) | −1.15340 | + | 1.99775i | −0.109972 | + | 0.190478i | ||||
\(111\) | 5.30334 | + | 10.7280i | 0.503371 | + | 1.01826i | ||||
\(112\) | −0.618268 | − | 2.57250i | −0.0584209 | − | 0.243078i | ||||
\(113\) | − | 4.45505i | − | 0.419096i | −0.977798 | − | 0.209548i | \(-0.932801\pi\) | ||
0.977798 | − | 0.209548i | \(-0.0671992\pi\) | |||||||
\(114\) | −13.0622 | − | 0.843477i | −1.22339 | − | 0.0789988i | ||||
\(115\) | −5.51880 | + | 3.18628i | −0.514631 | + | 0.297122i | ||||
\(116\) | 3.32150 | − | 1.91767i | 0.308393 | − | 0.178051i | ||||
\(117\) | 13.8494 | − | 5.76797i | 1.28038 | − | 0.533249i | ||||
\(118\) | − | 9.93145i | − | 0.914264i | ||||||
\(119\) | 15.9888 | + | 4.73184i | 1.46569 | + | 0.433767i | ||||
\(120\) | 1.55269 | − | 0.767566i | 0.141740 | − | 0.0700689i | ||||
\(121\) | −2.83934 | + | 4.91787i | −0.258121 | + | 0.447079i | ||||
\(122\) | −2.99184 | − | 5.18202i | −0.270868 | − | 0.469158i | ||||
\(123\) | −9.41063 | + | 14.1135i | −0.848528 | + | 1.27257i | ||||
\(124\) | −3.79452 | − | 2.19077i | −0.340758 | − | 0.196737i | ||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 4.67936 | + | 6.41121i | 0.416871 | + | 0.571156i | ||||
\(127\) | −1.83694 | −0.163002 | −0.0815011 | − | 0.996673i | \(-0.525971\pi\) | ||||
−0.0815011 | + | 0.996673i | \(0.525971\pi\) | |||||||
\(128\) | −0.866025 | − | 0.500000i | −0.0765466 | − | 0.0441942i | ||||
\(129\) | −2.45293 | + | 3.67875i | −0.215968 | + | 0.323896i | ||||
\(130\) | −2.50042 | − | 4.33086i | −0.219301 | − | 0.379841i | ||||
\(131\) | −2.76942 | + | 4.79677i | −0.241965 | + | 0.419096i | −0.961274 | − | 0.275595i | \(-0.911125\pi\) |
0.719309 | + | 0.694690i | \(0.244459\pi\) | |||||||
\(132\) | −3.58174 | + | 1.77062i | −0.311751 | + | 0.154113i | ||||
\(133\) | −19.4408 | + | 4.67236i | −1.68573 | + | 0.405145i | ||||
\(134\) | 2.76716i | 0.239047i | ||||||||
\(135\) | −3.41473 | + | 3.91658i | −0.293893 | + | 0.337086i | ||||
\(136\) | 5.45795 | − | 3.15115i | 0.468015 | − | 0.270209i | ||||
\(137\) | 1.07477 | − | 0.620520i | 0.0918240 | − | 0.0530146i | −0.453385 | − | 0.891315i | \(-0.649784\pi\) |
0.545209 | + | 0.838300i | \(0.316450\pi\) | |||||||
\(138\) | −11.0147 | − | 0.711259i | −0.937630 | − | 0.0605464i | ||||
\(139\) | − | 12.5344i | − | 1.06315i | −0.847011 | − | 0.531576i | \(-0.821600\pi\) | ||
0.847011 | − | 0.531576i | \(-0.178400\pi\) | |||||||
\(140\) | 1.91871 | − | 1.82168i | 0.162161 | − | 0.153960i | ||||
\(141\) | −1.27173 | − | 2.57255i | −0.107099 | − | 0.216647i | ||||
\(142\) | −1.42955 | + | 2.47605i | −0.119965 | + | 0.207786i | ||||
\(143\) | 5.76797 | + | 9.99042i | 0.482342 | + | 0.835441i | ||||
\(144\) | 2.97509 | + | 0.385834i | 0.247924 | + | 0.0321529i | ||||
\(145\) | 3.32150 | + | 1.91767i | 0.275835 | + | 0.159254i | ||||
\(146\) | −3.68177 | −0.304706 | ||||||||
\(147\) | 9.72523 | + | 7.24016i | 0.802124 | + | 0.597158i | ||||
\(148\) | 6.90930 | 0.567941 | ||||||||
\(149\) | 13.5058 | + | 7.79757i | 1.10644 | + | 0.638802i | 0.937904 | − | 0.346894i | \(-0.112764\pi\) |
0.168533 | + | 0.985696i | \(0.446097\pi\) | |||||||
\(150\) | 1.44108 | + | 0.960885i | 0.117663 | + | 0.0784559i | ||||
\(151\) | −1.51958 | − | 2.63198i | −0.123661 | − | 0.214188i | 0.797548 | − | 0.603256i | \(-0.206130\pi\) |
−0.921209 | + | 0.389068i | \(0.872797\pi\) | |||||||
\(152\) | −3.77859 | + | 6.54470i | −0.306484 | + | 0.530846i | ||||
\(153\) | −11.4808 | + | 15.0220i | −0.928168 | + | 1.21446i | ||||
\(154\) | −4.42609 | + | 4.20226i | −0.356665 | + | 0.338628i | ||||
\(155\) | − | 4.38153i | − | 0.351933i | ||||||
\(156\) | 0.558158 | − | 8.64371i | 0.0446884 | − | 0.692050i | ||||
\(157\) | 13.7050 | − | 7.91260i | 1.09378 | − | 0.631494i | 0.159200 | − | 0.987246i | \(-0.449109\pi\) |
0.934580 | + | 0.355752i | \(0.115775\pi\) | |||||||
\(158\) | −2.21607 | + | 1.27945i | −0.176301 | + | 0.101787i | ||||
\(159\) | 0.363052 | − | 5.62228i | 0.0287919 | − | 0.445876i | ||||
\(160\) | − | 1.00000i | − | 0.0790569i | ||||||
\(161\) | −16.3934 | + | 3.93995i | −1.29198 | + | 0.310512i | ||||
\(162\) | −8.68427 | + | 2.36293i | −0.682301 | + | 0.185649i | ||||
\(163\) | 4.30841 | − | 7.46238i | 0.337461 | − | 0.584499i | −0.646494 | − | 0.762919i | \(-0.723765\pi\) |
0.983954 | + | 0.178420i | \(0.0570987\pi\) | |||||||
\(164\) | 4.89686 | + | 8.48160i | 0.382380 | + | 0.662302i | ||||
\(165\) | −3.32428 | − | 2.21657i | −0.258794 | − | 0.172560i | ||||
\(166\) | −1.59126 | − | 0.918714i | −0.123506 | − | 0.0713060i | ||||
\(167\) | −8.64948 | −0.669317 | −0.334658 | − | 0.942339i | \(-0.608621\pi\) | ||||
−0.334658 | + | 0.942339i | \(0.608621\pi\) | |||||||
\(168\) | 4.51544 | − | 0.781523i | 0.348374 | − | 0.0602958i | ||||
\(169\) | −12.0084 | −0.923724 | ||||||||
\(170\) | 5.45795 | + | 3.15115i | 0.418606 | + | 0.241682i | ||||
\(171\) | 2.91582 | − | 22.4832i | 0.222978 | − | 1.71934i | ||||
\(172\) | 1.27639 | + | 2.21077i | 0.0973239 | + | 0.168570i | ||||
\(173\) | 8.96573 | − | 15.5291i | 0.681652 | − | 1.18066i | −0.292825 | − | 0.956166i | \(-0.594595\pi\) |
0.974477 | − | 0.224489i | \(-0.0720713\pi\) | |||||||
\(174\) | 2.94387 | + | 5.95508i | 0.223174 | + | 0.451454i | ||||
\(175\) | 2.53698 | + | 0.750813i | 0.191778 | + | 0.0567561i | ||||
\(176\) | 2.30680i | 0.173882i | ||||||||
\(177\) | 17.1660 | + | 1.10848i | 1.29028 | + | 0.0833182i | ||||
\(178\) | −5.09894 | + | 2.94387i | −0.382181 | + | 0.220653i | ||||
\(179\) | 10.4070 | − | 6.00848i | 0.777855 | − | 0.449095i | −0.0578145 | − | 0.998327i | \(-0.518413\pi\) |
0.835670 | + | 0.549233i | \(0.185080\pi\) | |||||||
\(180\) | 1.15340 | + | 2.76942i | 0.0859694 | + | 0.206420i | ||||
\(181\) | − | 9.52612i | − | 0.708071i | −0.935232 | − | 0.354036i | \(-0.884809\pi\) | ||
0.935232 | − | 0.354036i | \(-0.115191\pi\) | |||||||
\(182\) | −3.09186 | − | 12.8647i | −0.229184 | − | 0.953591i | ||||
\(183\) | 9.29079 | − | 4.59287i | 0.686795 | − | 0.339514i | ||||
\(184\) | −3.18628 | + | 5.51880i | −0.234896 | + | 0.406851i | ||||
\(185\) | 3.45465 | + | 5.98363i | 0.253991 | + | 0.439925i | ||||
\(186\) | 4.21015 | − | 6.31412i | 0.308703 | − | 0.462974i | ||||
\(187\) | −12.5904 | − | 7.26907i | −0.920701 | − | 0.531567i | ||||
\(188\) | −1.65683 | −0.120837 | ||||||||
\(189\) | −11.6037 | + | 7.37248i | −0.844047 | + | 0.536269i | ||||
\(190\) | −7.55717 | −0.548255 | ||||||||
\(191\) | 4.30564 | + | 2.48586i | 0.311545 | + | 0.179871i | 0.647618 | − | 0.761965i | \(-0.275765\pi\) |
−0.336073 | + | 0.941836i | \(0.609099\pi\) | |||||||
\(192\) | 0.960885 | − | 1.44108i | 0.0693459 | − | 0.104001i | ||||
\(193\) | −3.01660 | − | 5.22491i | −0.217140 | − | 0.376097i | 0.736793 | − | 0.676119i | \(-0.236339\pi\) |
−0.953932 | + | 0.300022i | \(0.903006\pi\) | |||||||
\(194\) | 2.30861 | − | 3.99864i | 0.165749 | − | 0.287085i | ||||
\(195\) | 7.76475 | − | 3.83848i | 0.556045 | − | 0.274879i | ||||
\(196\) | 6.23549 | − | 3.18099i | 0.445392 | − | 0.227213i | ||||
\(197\) | 14.2144i | 1.01273i | 0.862318 | + | 0.506366i | \(0.169012\pi\) | ||||
−0.862318 | + | 0.506366i | \(0.830988\pi\) | |||||||
\(198\) | −2.66066 | − | 6.38849i | −0.189085 | − | 0.454010i | ||||
\(199\) | 1.94932 | − | 1.12544i | 0.138183 | − | 0.0797802i | −0.429315 | − | 0.903155i | \(-0.641245\pi\) |
0.567498 | + | 0.823375i | \(0.307911\pi\) | |||||||
\(200\) | 0.866025 | − | 0.500000i | 0.0612372 | − | 0.0353553i | ||||
\(201\) | −4.78291 | − | 0.308851i | −0.337360 | − | 0.0217847i | ||||
\(202\) | − | 11.3140i | − | 0.796053i | ||||||
\(203\) | 6.98677 | + | 7.35891i | 0.490375 | + | 0.516494i | ||||
\(204\) | 4.83743 | + | 9.78550i | 0.338688 | + | 0.685122i | ||||
\(205\) | −4.89686 | + | 8.48160i | −0.342011 | + | 0.592381i | ||||
\(206\) | 3.68203 | + | 6.37747i | 0.256540 | + | 0.444339i | ||||
\(207\) | 2.45875 | − | 18.9589i | 0.170895 | − | 1.31774i | ||||
\(208\) | −4.33086 | − | 2.50042i | −0.300291 | − | 0.173373i | ||||
\(209\) | 17.4329 | 1.20586 | ||||||||
\(210\) | 2.93454 | + | 3.51973i | 0.202502 | + | 0.242884i | ||||
\(211\) | 27.6034 | 1.90029 | 0.950147 | − | 0.311804i | \(-0.100933\pi\) | ||||
0.950147 | + | 0.311804i | \(0.100933\pi\) | |||||||
\(212\) | −2.81699 | − | 1.62639i | −0.193472 | − | 0.111701i | ||||
\(213\) | −4.12018 | − | 2.74726i | −0.282310 | − | 0.188239i | ||||
\(214\) | −4.20937 | − | 7.29084i | −0.287747 | − | 0.498392i | ||||
\(215\) | −1.27639 | + | 2.21077i | −0.0870492 | + | 0.150774i | ||||
\(216\) | −0.998953 | + | 5.09922i | −0.0679701 | + | 0.346958i | ||||
\(217\) | 3.28971 | − | 11.1159i | 0.223320 | − | 0.754594i | ||||
\(218\) | 6.66311i | 0.451283i | ||||||||
\(219\) | 0.410933 | − | 6.36376i | 0.0277683 | − | 0.430023i | ||||
\(220\) | −1.99775 | + | 1.15340i | −0.134688 | + | 0.0777622i | ||||
\(221\) | 27.2943 | − | 15.7584i | 1.83602 | − | 1.06002i | ||||
\(222\) | −0.771166 | + | 11.9424i | −0.0517573 | + | 0.801520i | ||||
\(223\) | − | 23.0777i | − | 1.54539i | −0.634775 | − | 0.772697i | \(-0.718907\pi\) | ||
0.634775 | − | 0.772697i | \(-0.281093\pi\) | |||||||
\(224\) | 0.750813 | − | 2.53698i | 0.0501658 | − | 0.169509i | ||||
\(225\) | −1.82168 | + | 2.38358i | −0.121446 | + | 0.158905i | ||||
\(226\) | 2.22752 | − | 3.85818i | 0.148173 | − | 0.256643i | ||||
\(227\) | −10.0175 | − | 17.3509i | −0.664887 | − | 1.15162i | −0.979316 | − | 0.202337i | \(-0.935146\pi\) |
0.314429 | − | 0.949281i | \(-0.398187\pi\) | |||||||
\(228\) | −10.8905 | − | 7.26157i | −0.721238 | − | 0.480909i | ||||
\(229\) | 24.9111 | + | 14.3824i | 1.64617 | + | 0.950417i | 0.978575 | + | 0.205892i | \(0.0660097\pi\) |
0.667595 | + | 0.744524i | \(0.267324\pi\) | |||||||
\(230\) | −6.37256 | −0.420194 | ||||||||
\(231\) | −6.76940 | − | 8.11931i | −0.445394 | − | 0.534211i | ||||
\(232\) | 3.83533 | 0.251802 | ||||||||
\(233\) | −22.2668 | − | 12.8558i | −1.45875 | − | 0.842209i | −0.459799 | − | 0.888023i | \(-0.652079\pi\) |
−0.998950 | + | 0.0458133i | \(0.985412\pi\) | |||||||
\(234\) | 14.8779 | + | 1.92950i | 0.972601 | + | 0.126135i | ||||
\(235\) | −0.828416 | − | 1.43486i | −0.0540399 | − | 0.0935999i | ||||
\(236\) | 4.96573 | − | 8.60089i | 0.323241 | − | 0.559870i | ||||
\(237\) | −1.96412 | − | 3.97317i | −0.127583 | − | 0.258085i | ||||
\(238\) | 11.4808 | + | 12.0923i | 0.744190 | + | 0.783828i | ||||
\(239\) | 10.7220i | 0.693551i | 0.937948 | + | 0.346776i | \(0.112723\pi\) | ||||
−0.937948 | + | 0.346776i | \(0.887277\pi\) | |||||||
\(240\) | 1.72845 | + | 0.111613i | 0.111571 | + | 0.00720457i | ||||
\(241\) | 1.02594 | − | 0.592325i | 0.0660864 | − | 0.0381550i | −0.466593 | − | 0.884472i | \(-0.654519\pi\) |
0.532679 | + | 0.846317i | \(0.321185\pi\) | |||||||
\(242\) | −4.91787 | + | 2.83934i | −0.316133 | + | 0.182519i | ||||
\(243\) | −3.11493 | − | 15.2741i | −0.199823 | − | 0.979832i | ||||
\(244\) | − | 5.98368i | − | 0.383066i | ||||||
\(245\) | 5.87256 | + | 3.80960i | 0.375184 | + | 0.243386i | ||||
\(246\) | −15.2066 | + | 7.51732i | −0.969536 | + | 0.479287i | ||||
\(247\) | −18.8961 | + | 32.7290i | −1.20233 | + | 2.08250i | ||||
\(248\) | −2.19077 | − | 3.79452i | −0.139114 | − | 0.240952i | ||||
\(249\) | 1.76556 | − | 2.64787i | 0.111888 | − | 0.167802i | ||||
\(250\) | 0.866025 | + | 0.500000i | 0.0547723 | + | 0.0316228i | ||||
\(251\) | −14.3689 | −0.906958 | −0.453479 | − | 0.891267i | \(-0.649817\pi\) | ||||
−0.453479 | + | 0.891267i | \(0.649817\pi\) | |||||||
\(252\) | 0.846843 | + | 7.89195i | 0.0533461 | + | 0.497146i | ||||
\(253\) | 14.7002 | 0.924195 | ||||||||
\(254\) | −1.59084 | − | 0.918471i | −0.0998181 | − | 0.0576300i | ||||
\(255\) | −6.05578 | + | 9.08209i | −0.379228 | + | 0.568742i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 8.26802 | − | 14.3206i | 0.515745 | − | 0.893297i | −0.484088 | − | 0.875019i | \(-0.660848\pi\) |
0.999833 | − | 0.0182774i | \(-0.00581819\pi\) | |||||||
\(258\) | −3.96368 | + | 1.95943i | −0.246768 | + | 0.121989i | ||||
\(259\) | 4.27180 | + | 17.7742i | 0.265437 | + | 1.10443i | ||||
\(260\) | − | 5.00084i | − | 0.310139i | ||||||
\(261\) | −10.6216 | + | 4.42368i | −0.657463 | + | 0.273819i | ||||
\(262\) | −4.79677 | + | 2.76942i | −0.296345 | + | 0.171095i | ||||
\(263\) | −26.7948 | + | 15.4700i | −1.65224 | + | 0.953920i | −0.676089 | + | 0.736820i | \(0.736327\pi\) |
−0.976149 | + | 0.217100i | \(0.930340\pi\) | |||||||
\(264\) | −3.98719 | − | 0.257468i | −0.245395 | − | 0.0158461i | ||||
\(265\) | − | 3.25278i | − | 0.199817i | ||||||
\(266\) | −19.1724 | − | 5.67402i | −1.17554 | − | 0.347897i | ||||
\(267\) | −4.51923 | − | 9.14184i | −0.276573 | − | 0.559471i | ||||
\(268\) | −1.38358 | + | 2.39643i | −0.0845157 | + | 0.146386i | ||||
\(269\) | −2.05211 | − | 3.55436i | −0.125119 | − | 0.216713i | 0.796660 | − | 0.604427i | \(-0.206598\pi\) |
−0.921780 | + | 0.387714i | \(0.873265\pi\) | |||||||
\(270\) | −4.91553 | + | 1.68449i | −0.299150 | + | 0.102515i | ||||
\(271\) | −7.86071 | − | 4.53838i | −0.477504 | − | 0.275687i | 0.241872 | − | 0.970308i | \(-0.422239\pi\) |
−0.719376 | + | 0.694621i | \(0.755572\pi\) | |||||||
\(272\) | 6.30230 | 0.382133 | ||||||||
\(273\) | 22.5810 | − | 3.90827i | 1.36666 | − | 0.236539i | ||||
\(274\) | 1.24104 | 0.0749740 | ||||||||
\(275\) | −1.99775 | − | 1.15340i | −0.120469 | − | 0.0695527i | ||||
\(276\) | −9.18334 | − | 6.12330i | −0.552772 | − | 0.368579i | ||||
\(277\) | −0.108238 | − | 0.187473i | −0.00650338 | − | 0.0112642i | 0.862755 | − | 0.505622i | \(-0.168737\pi\) |
−0.869259 | + | 0.494357i | \(0.835403\pi\) | |||||||
\(278\) | 6.26718 | − | 10.8551i | 0.375881 | − | 0.651044i | ||||
\(279\) | 10.4437 | + | 7.98177i | 0.625250 | + | 0.477856i | ||||
\(280\) | 2.57250 | − | 0.618268i | 0.153736 | − | 0.0369486i | ||||
\(281\) | 18.8498i | 1.12448i | 0.826973 | + | 0.562241i | \(0.190061\pi\) | ||||
−0.826973 | + | 0.562241i | \(0.809939\pi\) | |||||||
\(282\) | 0.184924 | − | 2.86375i | 0.0110120 | − | 0.170534i | ||||
\(283\) | −1.73059 | + | 0.999159i | −0.102873 | + | 0.0593939i | −0.550554 | − | 0.834800i | \(-0.685583\pi\) |
0.447681 | + | 0.894193i | \(0.352250\pi\) | |||||||
\(284\) | −2.47605 | + | 1.42955i | −0.146927 | + | 0.0848281i | ||||
\(285\) | 0.843477 | − | 13.0622i | 0.0499633 | − | 0.773738i | ||||
\(286\) | 11.5359i | 0.682135i | ||||||||
\(287\) | −18.7913 | + | 17.8411i | −1.10922 | + | 1.05312i | ||||
\(288\) | 2.38358 | + | 1.82168i | 0.140454 | + | 0.107344i | ||||
\(289\) | −11.3595 | + | 19.6752i | −0.668204 | + | 1.15736i | ||||
\(290\) | 1.91767 | + | 3.32150i | 0.112609 | + | 0.195045i | ||||
\(291\) | 6.65378 | + | 4.43662i | 0.390051 | + | 0.260080i | ||||
\(292\) | −3.18851 | − | 1.84089i | −0.186593 | − | 0.107730i | ||||
\(293\) | 9.28117 | 0.542212 | 0.271106 | − | 0.962550i | \(-0.412611\pi\) | ||||
0.271106 | + | 0.962550i | \(0.412611\pi\) | |||||||
\(294\) | 4.80222 | + | 11.1328i | 0.280071 | + | 0.649277i | ||||
\(295\) | 9.93145 | 0.578232 | ||||||||
\(296\) | 5.98363 | + | 3.45465i | 0.347791 | + | 0.200797i | ||||
\(297\) | 11.3392 | − | 3.88579i | 0.657965 | − | 0.225476i | ||||
\(298\) | 7.79757 | + | 13.5058i | 0.451701 | + | 0.782370i | ||||
\(299\) | −15.9341 | + | 27.5986i | −0.921492 | + | 1.59607i | ||||
\(300\) | 0.767566 | + | 1.55269i | 0.0443154 | + | 0.0896445i | ||||
\(301\) | −4.89806 | + | 4.65037i | −0.282319 | + | 0.268043i | ||||
\(302\) | − | 3.03915i | − | 0.174883i | ||||||
\(303\) | 19.5558 | + | 1.26279i | 1.12345 | + | 0.0725454i | ||||
\(304\) | −6.54470 | + | 3.77859i | −0.375365 | + | 0.216717i | ||||
\(305\) | 5.18202 | − | 2.99184i | 0.296721 | − | 0.171312i | ||||
\(306\) | −17.4537 | + | 7.26907i | −0.997761 | + | 0.415545i | ||||
\(307\) | 26.9282i | 1.53687i | 0.639927 | + | 0.768436i | \(0.278965\pi\) | ||||
−0.639927 | + | 0.768436i | \(0.721035\pi\) | |||||||
\(308\) | −5.93424 | + | 1.42622i | −0.338135 | + | 0.0812665i | ||||
\(309\) | −11.4341 | + | 5.65241i | −0.650464 | + | 0.321554i | ||||
\(310\) | 2.19077 | − | 3.79452i | 0.124427 | − | 0.215514i | ||||
\(311\) | 1.41065 | + | 2.44331i | 0.0799905 | + | 0.138548i | 0.903246 | − | 0.429124i | \(-0.141178\pi\) |
−0.823255 | + | 0.567672i | \(0.807844\pi\) | |||||||
\(312\) | 4.80523 | − | 7.20659i | 0.272043 | − | 0.407993i | ||||
\(313\) | −9.90967 | − | 5.72135i | −0.560128 | − | 0.323390i | 0.193069 | − | 0.981185i | \(-0.438156\pi\) |
−0.753197 | + | 0.657795i | \(0.771489\pi\) | |||||||
\(314\) | 15.8252 | 0.893068 | ||||||||
\(315\) | −6.41121 | + | 4.67936i | −0.361231 | + | 0.263652i | ||||
\(316\) | −2.55889 | −0.143949 | ||||||||
\(317\) | −8.06254 | − | 4.65491i | −0.452837 | − | 0.261446i | 0.256190 | − | 0.966626i | \(-0.417533\pi\) |
−0.709028 | + | 0.705181i | \(0.750866\pi\) | |||||||
\(318\) | 3.12555 | − | 4.68751i | 0.175272 | − | 0.262862i | ||||
\(319\) | −4.42368 | − | 7.66203i | −0.247678 | − | 0.428991i | ||||
\(320\) | 0.500000 | − | 0.866025i | 0.0279508 | − | 0.0484123i | ||||
\(321\) | 13.0717 | − | 6.46194i | 0.729590 | − | 0.360670i | ||||
\(322\) | −16.1671 | − | 4.78460i | −0.900956 | − | 0.266635i | ||||
\(323\) | − | 47.6275i | − | 2.65007i | ||||||
\(324\) | −8.70226 | − | 2.29578i | −0.483459 | − | 0.127543i | ||||
\(325\) | 4.33086 | − | 2.50042i | 0.240233 | − | 0.138698i | ||||
\(326\) | 7.46238 | − | 4.30841i | 0.413303 | − | 0.238621i | ||||
\(327\) | −11.5169 | − | 0.743688i | −0.636884 | − | 0.0411261i | ||||
\(328\) | 9.79371i | 0.540767i | ||||||||
\(329\) | −1.02437 | − | 4.26220i | −0.0564752 | − | 0.234983i | ||||
\(330\) | −1.77062 | − | 3.58174i | −0.0974695 | − | 0.197168i | ||||
\(331\) | −9.14801 | + | 15.8448i | −0.502820 | + | 0.870910i | 0.497175 | + | 0.867650i | \(0.334371\pi\) |
−0.999995 | + | 0.00325921i | \(0.998963\pi\) | |||||||
\(332\) | −0.918714 | − | 1.59126i | −0.0504210 | − | 0.0873317i | ||||
\(333\) | −20.5558 | − | 2.66584i | −1.12645 | − | 0.146087i | ||||
\(334\) | −7.49067 | − | 4.32474i | −0.409871 | − | 0.236639i | ||||
\(335\) | −2.76716 | −0.151186 | ||||||||
\(336\) | 4.30125 | + | 1.58090i | 0.234652 | + | 0.0862453i | ||||
\(337\) | 7.84516 | 0.427353 | 0.213676 | − | 0.976904i | \(-0.431456\pi\) | ||||
0.213676 | + | 0.976904i | \(0.431456\pi\) | |||||||
\(338\) | −10.3996 | − | 6.00420i | −0.565663 | − | 0.326586i | ||||
\(339\) | 6.42006 | + | 4.28079i | 0.348690 | + | 0.232500i | ||||
\(340\) | 3.15115 | + | 5.45795i | 0.170895 | + | 0.295999i | ||||
\(341\) | −5.05366 | + | 8.75320i | −0.273671 | + | 0.474012i | ||||
\(342\) | 13.7668 | − | 18.0131i | 0.744423 | − | 0.974039i | ||||
\(343\) | 12.0383 | + | 14.0741i | 0.650006 | + | 0.759929i | ||||
\(344\) | 2.55278i | 0.137637i | ||||||||
\(345\) | 0.711259 | − | 11.0147i | 0.0382929 | − | 0.593009i | ||||
\(346\) | 15.5291 | − | 8.96573i | 0.834849 | − | 0.482000i | ||||
\(347\) | −0.201172 | + | 0.116147i | −0.0107995 | + | 0.00623509i | −0.505390 | − | 0.862891i | \(-0.668651\pi\) |
0.494591 | + | 0.869126i | \(0.335318\pi\) | |||||||
\(348\) | −0.428072 | + | 6.62919i | −0.0229471 | + | 0.355362i | ||||
\(349\) | 11.5685i | 0.619249i | 0.950859 | + | 0.309624i | \(0.100203\pi\) | ||||
−0.950859 | + | 0.309624i | \(0.899797\pi\) | |||||||
\(350\) | 1.82168 | + | 1.91871i | 0.0973732 | + | 0.102560i | ||||
\(351\) | −4.99561 | + | 25.5004i | −0.266646 | + | 1.36111i | ||||
\(352\) | −1.15340 | + | 1.99775i | −0.0614764 | + | 0.106480i | ||||
\(353\) | 17.3537 | + | 30.0575i | 0.923646 | + | 1.59980i | 0.793725 | + | 0.608277i | \(0.208139\pi\) |
0.129921 | + | 0.991524i | \(0.458528\pi\) | |||||||
\(354\) | 14.3120 | + | 9.54298i | 0.760673 | + | 0.507204i | ||||
\(355\) | −2.47605 | − | 1.42955i | −0.131415 | − | 0.0758725i | ||||
\(356\) | −5.88774 | −0.312050 | ||||||||
\(357\) | −22.1824 | + | 18.4943i | −1.17401 | + | 0.978824i | ||||
\(358\) | 12.0170 | 0.635116 | ||||||||
\(359\) | 15.1834 | + | 8.76612i | 0.801347 | + | 0.462658i | 0.843942 | − | 0.536434i | \(-0.180229\pi\) |
−0.0425949 | + | 0.999092i | \(0.513562\pi\) | |||||||
\(360\) | −0.385834 | + | 2.97509i | −0.0203353 | + | 0.156801i | ||||
\(361\) | 19.0554 | + | 33.0050i | 1.00292 | + | 1.73710i | ||||
\(362\) | 4.76306 | − | 8.24987i | 0.250341 | − | 0.433603i | ||||
\(363\) | −4.35875 | − | 8.81721i | −0.228775 | − | 0.462783i | ||||
\(364\) | 3.75470 | − | 12.6870i | 0.196799 | − | 0.664982i | ||||
\(365\) | − | 3.68177i | − | 0.192713i | ||||||
\(366\) | 10.3425 | + | 0.667855i | 0.540611 | + | 0.0349093i | ||||
\(367\) | −8.69505 | + | 5.02009i | −0.453878 | + | 0.262047i | −0.709467 | − | 0.704739i | \(-0.751064\pi\) |
0.255589 | + | 0.966786i | \(0.417731\pi\) | |||||||
\(368\) | −5.51880 | + | 3.18628i | −0.287687 | + | 0.166096i | ||||
\(369\) | −11.2961 | − | 27.1229i | −0.588050 | − | 1.41196i | ||||
\(370\) | 6.90930i | 0.359197i | ||||||||
\(371\) | 2.44223 | − | 8.25225i | 0.126794 | − | 0.428436i | ||||
\(372\) | 6.80316 | − | 3.36311i | 0.352727 | − | 0.174369i | ||||
\(373\) | 0.00241034 | − | 0.00417483i | 0.000124803 | − | 0.000216164i | −0.865963 | − | 0.500108i | \(-0.833294\pi\) |
0.866088 | + | 0.499892i | \(0.166627\pi\) | |||||||
\(374\) | −7.26907 | − | 12.5904i | −0.375875 | − | 0.651034i | ||||
\(375\) | −0.960885 | + | 1.44108i | −0.0496199 | + | 0.0744168i | ||||
\(376\) | −1.43486 | − | 0.828416i | −0.0739972 | − | 0.0427223i | ||||
\(377\) | 19.1799 | 0.987815 | ||||||||
\(378\) | −13.7354 | + | 0.582885i | −0.706471 | + | 0.0299803i | ||||
\(379\) | 18.6572 | 0.958356 | 0.479178 | − | 0.877718i | \(-0.340935\pi\) | ||||
0.479178 | + | 0.877718i | \(0.340935\pi\) | |||||||
\(380\) | −6.54470 | − | 3.77859i | −0.335736 | − | 0.193837i | ||||
\(381\) | 1.76509 | − | 2.64717i | 0.0904283 | − | 0.135619i | ||||
\(382\) | 2.48586 | + | 4.30564i | 0.127188 | + | 0.220296i | ||||
\(383\) | −9.42316 | + | 16.3214i | −0.481501 | + | 0.833984i | −0.999775 | − | 0.0212308i | \(-0.993242\pi\) |
0.518274 | + | 0.855215i | \(0.326575\pi\) | |||||||
\(384\) | 1.55269 | − | 0.767566i | 0.0792353 | − | 0.0391697i | ||||
\(385\) | −4.20226 | − | 4.42609i | −0.214167 | − | 0.225574i | ||||
\(386\) | − | 6.03321i | − | 0.307082i | ||||||
\(387\) | −2.94438 | − | 7.06972i | −0.149671 | − | 0.359374i | ||||
\(388\) | 3.99864 | − | 2.30861i | 0.203000 | − | 0.117202i | ||||
\(389\) | −9.40510 | + | 5.43003i | −0.476857 | + | 0.275314i | −0.719106 | − | 0.694901i | \(-0.755448\pi\) |
0.242249 | + | 0.970214i | \(0.422115\pi\) | |||||||
\(390\) | 8.64371 | + | 0.558158i | 0.437691 | + | 0.0282634i | ||||
\(391\) | − | 40.1618i | − | 2.03107i | ||||||
\(392\) | 6.99059 | + | 0.362928i | 0.353078 | + | 0.0183306i | ||||
\(393\) | −4.25142 | − | 8.60008i | −0.214456 | − | 0.433817i | ||||
\(394\) | −7.10719 | + | 12.3100i | −0.358055 | + | 0.620170i | ||||
\(395\) | −1.27945 | − | 2.21607i | −0.0643760 | − | 0.111502i | ||||
\(396\) | 0.890043 | − | 6.86293i | 0.0447263 | − | 0.344875i | ||||
\(397\) | −23.4180 | − | 13.5204i | −1.17532 | − | 0.678570i | −0.220391 | − | 0.975412i | \(-0.570733\pi\) |
−0.954927 | + | 0.296841i | \(0.904067\pi\) | |||||||
\(398\) | 2.25088 | 0.112826 | ||||||||
\(399\) | 11.9472 | − | 32.5053i | 0.598106 | − | 1.62730i | ||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −21.2396 | − | 12.2627i | −1.06066 | − | 0.612371i | −0.135043 | − | 0.990840i | \(-0.543117\pi\) |
−0.925614 | + | 0.378469i | \(0.876451\pi\) | |||||||
\(402\) | −3.98769 | − | 2.65893i | −0.198888 | − | 0.132615i | ||||
\(403\) | −10.9557 | − | 18.9758i | −0.545741 | − | 0.945251i | ||||
\(404\) | 5.65702 | − | 9.79825i | 0.281447 | − | 0.487481i | ||||
\(405\) | −2.36293 | − | 8.68427i | −0.117415 | − | 0.431525i | ||||
\(406\) | 2.37127 | + | 9.86639i | 0.117684 | + | 0.489661i | ||||
\(407\) | − | 15.9384i | − | 0.790036i | ||||||
\(408\) | −0.703417 | + | 10.8932i | −0.0348243 | + | 0.539294i | ||||
\(409\) | 4.67954 | − | 2.70173i | 0.231388 | − | 0.133592i | −0.379824 | − | 0.925059i | \(-0.624015\pi\) |
0.611212 | + | 0.791467i | \(0.290682\pi\) | |||||||
\(410\) | −8.48160 | + | 4.89686i | −0.418876 | + | 0.241838i | ||||
\(411\) | −0.138516 | + | 2.14508i | −0.00683249 | + | 0.105809i | ||||
\(412\) | 7.36407i | 0.362802i | ||||||||
\(413\) | 25.1959 | + | 7.45666i | 1.23981 | + | 0.366918i | ||||
\(414\) | 11.6088 | − | 15.1895i | 0.570541 | − | 0.746524i | ||||
\(415\) | 0.918714 | − | 1.59126i | 0.0450979 | − | 0.0781119i | ||||
\(416\) | −2.50042 | − | 4.33086i | −0.122593 | − | 0.212338i | ||||
\(417\) | 18.0630 | + | 12.0441i | 0.884548 | + | 0.589801i | ||||
\(418\) | 15.0973 | + | 8.71645i | 0.738434 | + | 0.426335i | ||||
\(419\) | −28.2930 | −1.38220 | −0.691101 | − | 0.722758i | \(-0.742874\pi\) | ||||
−0.691101 | + | 0.722758i | \(0.742874\pi\) | |||||||
\(420\) | 0.781523 | + | 4.51544i | 0.0381344 | + | 0.220331i | ||||
\(421\) | −25.1687 | −1.22665 | −0.613323 | − | 0.789832i | \(-0.710168\pi\) | ||||
−0.613323 | + | 0.789832i | \(0.710168\pi\) | |||||||
\(422\) | 23.9052 | + | 13.8017i | 1.16369 | + | 0.671855i | ||||
\(423\) | 4.92922 | + | 0.639263i | 0.239667 | + | 0.0310820i | ||||
\(424\) | −1.62639 | − | 2.81699i | −0.0789846 | − | 0.136805i | ||||
\(425\) | −3.15115 | + | 5.45795i | −0.152853 | + | 0.264749i | ||||
\(426\) | −2.19455 | − | 4.43929i | −0.106326 | − | 0.215084i | ||||
\(427\) | 15.3930 | − | 3.69952i | 0.744919 | − | 0.179032i | ||||
\(428\) | − | 8.41874i | − | 0.406935i | ||||||
\(429\) | −19.9393 | − | 1.28756i | −0.962679 | − | 0.0621639i | ||||
\(430\) | −2.21077 | + | 1.27639i | −0.106613 | + | 0.0615531i | ||||
\(431\) | −9.71524 | + | 5.60910i | −0.467967 | + | 0.270181i | −0.715388 | − | 0.698727i | \(-0.753750\pi\) |
0.247421 | + | 0.968908i | \(0.420417\pi\) | |||||||
\(432\) | −3.41473 | + | 3.91658i | −0.164291 | + | 0.188437i | ||||
\(433\) | − | 0.639592i | − | 0.0307368i | −0.999882 | − | 0.0153684i | \(-0.995108\pi\) | ||
0.999882 | − | 0.0153684i | \(-0.00489211\pi\) | |||||||
\(434\) | 8.40691 | − | 7.98177i | 0.403544 | − | 0.383137i | ||||
\(435\) | −5.95508 | + | 2.94387i | −0.285524 | + | 0.141148i | ||||
\(436\) | −3.33156 | + | 5.77043i | −0.159553 | + | 0.276353i | ||||
\(437\) | 24.0793 | + | 41.7065i | 1.15187 | + | 1.99509i | ||||
\(438\) | 3.53776 | − | 5.30571i | 0.169041 | − | 0.253517i | ||||
\(439\) | −11.3999 | − | 6.58174i | −0.544088 | − | 0.314129i | 0.202646 | − | 0.979252i | \(-0.435046\pi\) |
−0.746734 | + | 0.665123i | \(0.768379\pi\) | |||||||
\(440\) | −2.30680 | −0.109972 | ||||||||
\(441\) | −19.7784 | + | 7.05784i | −0.941831 | + | 0.336088i | ||||
\(442\) | 31.5168 | 1.49910 | ||||||||
\(443\) | −22.3821 | − | 12.9223i | −1.06341 | − | 0.613957i | −0.137033 | − | 0.990566i | \(-0.543757\pi\) |
−0.926372 | + | 0.376609i | \(0.877090\pi\) | |||||||
\(444\) | −6.63904 | + | 9.95683i | −0.315075 | + | 0.472530i | ||||
\(445\) | −2.94387 | − | 5.09894i | −0.139553 | − | 0.241713i | ||||
\(446\) | 11.5388 | − | 19.9858i | 0.546380 | − | 0.946357i | ||||
\(447\) | −24.2144 | + | 11.9703i | −1.14530 | + | 0.566176i | ||||
\(448\) | 1.91871 | − | 1.82168i | 0.0906507 | − | 0.0860665i | ||||
\(449\) | − | 28.3586i | − | 1.33833i | −0.743116 | − | 0.669163i | \(-0.766653\pi\) | ||
0.743116 | − | 0.669163i | \(-0.233347\pi\) | |||||||
\(450\) | −2.76942 | + | 1.15340i | −0.130552 | + | 0.0543718i | ||||
\(451\) | 19.5654 | − | 11.2961i | 0.921297 | − | 0.531911i | ||||
\(452\) | 3.85818 | − | 2.22752i | 0.181474 | − | 0.104774i | ||||
\(453\) | 5.25302 | + | 0.339208i | 0.246809 | + | 0.0159374i | ||||
\(454\) | − | 20.0351i | − | 0.940293i | ||||||
\(455\) | 12.8647 | − | 3.09186i | 0.603104 | − | 0.144949i | ||||
\(456\) | −5.80063 | − | 11.7339i | −0.271639 | − | 0.549492i | ||||
\(457\) | 14.5953 | − | 25.2797i | 0.682737 | − | 1.18254i | −0.291405 | − | 0.956600i | \(-0.594123\pi\) |
0.974142 | − | 0.225936i | \(-0.0725440\pi\) | |||||||
\(458\) | 14.3824 | + | 24.9111i | 0.672046 | + | 1.16402i | ||||
\(459\) | −10.6162 | − | 30.9792i | −0.495521 | − | 1.44598i | ||||
\(460\) | −5.51880 | − | 3.18628i | −0.257315 | − | 0.148561i | ||||
\(461\) | 31.0968 | 1.44832 | 0.724162 | − | 0.689630i | \(-0.242227\pi\) | ||||
0.724162 | + | 0.689630i | \(0.242227\pi\) | |||||||
\(462\) | −1.80282 | − | 10.4162i | −0.0838747 | − | 0.484607i | ||||
\(463\) | −33.4915 | −1.55648 | −0.778240 | − | 0.627967i | \(-0.783887\pi\) | ||||
−0.778240 | + | 0.627967i | \(0.783887\pi\) | |||||||
\(464\) | 3.32150 | + | 1.91767i | 0.154197 | + | 0.0890255i | ||||
\(465\) | 6.31412 | + | 4.21015i | 0.292810 | + | 0.195241i | ||||
\(466\) | −12.8558 | − | 22.2668i | −0.595532 | − | 1.03149i | ||||
\(467\) | −7.41254 | + | 12.8389i | −0.343012 | + | 0.594113i | −0.984990 | − | 0.172609i | \(-0.944780\pi\) |
0.641979 | + | 0.766722i | \(0.278114\pi\) | |||||||
\(468\) | 11.9199 | + | 9.10996i | 0.550998 | + | 0.421108i | ||||
\(469\) | −7.02025 | − | 2.07762i | −0.324165 | − | 0.0959357i | ||||
\(470\) | − | 1.65683i | − | 0.0764240i | ||||||
\(471\) | −1.76629 | + | 27.3531i | −0.0813865 | + | 1.26036i | ||||
\(472\) | 8.60089 | − | 4.96573i | 0.395888 | − | 0.228566i | ||||
\(473\) | 5.09982 | − | 2.94438i | 0.234490 | − | 0.135383i | ||||
\(474\) | 0.285605 | − | 4.42292i | 0.0131183 | − | 0.203152i | ||||
\(475\) | − | 7.55717i | − | 0.346747i | ||||||
\(476\) | 3.89651 | + | 16.2126i | 0.178596 | + | 0.743105i | ||||
\(477\) | 7.75328 | + | 5.92555i | 0.354998 | + | 0.271312i | ||||
\(478\) | −5.36102 | + | 9.28556i | −0.245207 | + | 0.424712i | ||||
\(479\) | −11.5223 | − | 19.9573i | −0.526469 | − | 0.911871i | −0.999524 | − | 0.0308386i | \(-0.990182\pi\) |
0.473055 | − | 0.881033i | \(-0.343151\pi\) | |||||||
\(480\) | 1.44108 | + | 0.960885i | 0.0657758 | + | 0.0438582i | ||||
\(481\) | 29.9232 | + | 17.2762i | 1.36438 | + | 0.787725i | ||||
\(482\) | 1.18465 | 0.0539593 | ||||||||
\(483\) | 10.0744 | − | 27.4100i | 0.458401 | − | 1.24720i | ||||
\(484\) | −5.67867 | −0.258121 | ||||||||
\(485\) | 3.99864 | + | 2.30861i | 0.181569 | + | 0.104829i | ||||
\(486\) | 4.93943 | − | 14.7852i | 0.224057 | − | 0.670670i | ||||
\(487\) | 5.31384 | + | 9.20383i | 0.240793 | + | 0.417066i | 0.960940 | − | 0.276756i | \(-0.0892592\pi\) |
−0.720147 | + | 0.693821i | \(0.755926\pi\) | |||||||
\(488\) | 2.99184 | − | 5.18202i | 0.135434 | − | 0.234579i | ||||
\(489\) | 6.61397 | + | 13.3792i | 0.299094 | + | 0.605030i | ||||
\(490\) | 3.18099 | + | 6.23549i | 0.143702 | + | 0.281691i | ||||
\(491\) | 22.4687i | 1.01400i | 0.861947 | + | 0.506998i | \(0.169245\pi\) | ||||
−0.861947 | + | 0.506998i | \(0.830755\pi\) | |||||||
\(492\) | −16.9279 | − | 1.09310i | −0.763171 | − | 0.0492809i | ||||
\(493\) | −20.9331 | + | 12.0857i | −0.942778 | + | 0.544313i | ||||
\(494\) | −32.7290 | + | 18.8961i | −1.47255 | + | 0.850176i | ||||
\(495\) | 6.38849 | − | 2.66066i | 0.287141 | − | 0.119588i | ||||
\(496\) | − | 4.38153i | − | 0.196737i | ||||||
\(497\) | −5.20837 | − | 5.48579i | −0.233627 | − | 0.246071i | ||||
\(498\) | 2.85295 | − | 1.41035i | 0.127844 | − | 0.0631992i | ||||
\(499\) | 19.8794 | − | 34.4322i | 0.889925 | − | 1.54140i | 0.0499622 | − | 0.998751i | \(-0.484090\pi\) |
0.839963 | − | 0.542644i | \(-0.182577\pi\) | |||||||
\(500\) | 0.500000 | + | 0.866025i | 0.0223607 | + | 0.0387298i | ||||
\(501\) | 8.31116 | − | 12.4646i | 0.371315 | − | 0.556875i | ||||
\(502\) | −12.4438 | − | 7.18445i | −0.555396 | − | 0.320658i | ||||
\(503\) | 18.6717 | 0.832530 | 0.416265 | − | 0.909243i | \(-0.363339\pi\) | ||||
0.416265 | + | 0.909243i | \(0.363339\pi\) | |||||||
\(504\) | −3.21259 | + | 7.25805i | −0.143100 | + | 0.323299i | ||||
\(505\) | 11.3140 | 0.503468 | ||||||||
\(506\) | 12.7308 | + | 7.35011i | 0.565952 | + | 0.326752i | ||||
\(507\) | 11.5387 | − | 17.3050i | 0.512452 | − | 0.768543i | ||||
\(508\) | −0.918471 | − | 1.59084i | −0.0407506 | − | 0.0705820i | ||||
\(509\) | 2.01643 | − | 3.49256i | 0.0893768 | − | 0.154805i | −0.817871 | − | 0.575402i | \(-0.804846\pi\) |
0.907248 | + | 0.420596i | \(0.138179\pi\) | |||||||
\(510\) | −9.78550 | + | 4.83743i | −0.433309 | + | 0.214205i | ||||
\(511\) | 2.76432 | − | 9.34059i | 0.122286 | − | 0.413203i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 29.5983 | + | 25.8057i | 1.30680 | + | 1.13935i | ||||
\(514\) | 14.3206 | − | 8.26802i | 0.631656 | − | 0.364687i | ||||
\(515\) | −6.37747 | + | 3.68203i | −0.281025 | + | 0.162250i | ||||
\(516\) | −4.41236 | − | 0.284923i | −0.194243 | − | 0.0125430i | ||||
\(517\) | 3.82198i | 0.168091i | ||||||||
\(518\) | −5.18759 | + | 17.5288i | −0.227930 | + | 0.770170i | ||||
\(519\) | 13.7636 | + | 27.8420i | 0.604154 | + | 1.22213i | ||||
\(520\) | 2.50042 | − | 4.33086i | 0.109651 | − | 0.189921i | ||||
\(521\) | −5.27733 | − | 9.14060i | −0.231204 | − | 0.400457i | 0.726959 | − | 0.686681i | \(-0.240933\pi\) |
−0.958163 | + | 0.286224i | \(0.907600\pi\) | |||||||
\(522\) | −11.4104 | − | 1.47980i | −0.499422 | − | 0.0647692i | ||||
\(523\) | −17.7815 | − | 10.2661i | −0.777529 | − | 0.448907i | 0.0580246 | − | 0.998315i | \(-0.481520\pi\) |
−0.835554 | + | 0.549408i | \(0.814853\pi\) | |||||||
\(524\) | −5.53883 | −0.241965 | ||||||||
\(525\) | −3.51973 | + | 2.93454i | −0.153613 | + | 0.128074i | ||||
\(526\) | −30.9400 | −1.34905 | ||||||||
\(527\) | 23.9142 | + | 13.8069i | 1.04172 | + | 0.601436i | ||||
\(528\) | −3.32428 | − | 2.21657i | −0.144671 | − | 0.0964638i | ||||
\(529\) | 8.80476 | + | 15.2503i | 0.382816 | + | 0.663056i | ||||
\(530\) | 1.62639 | − | 2.81699i | 0.0706459 | − | 0.122362i | ||||
\(531\) | −18.0920 | + | 23.6724i | −0.785125 | + | 1.02730i | ||||
\(532\) | −13.7668 | − | 14.5001i | −0.596866 | − | 0.628657i | ||||
\(533\) | 48.9768i | 2.12142i | ||||||||
\(534\) | 0.657147 | − | 10.1767i | 0.0284375 | − | 0.440388i | ||||
\(535\) | 7.29084 | − | 4.20937i | 0.315211 | − | 0.181987i | ||||
\(536\) | −2.39643 | + | 1.38358i | −0.103510 | + | 0.0597616i | ||||
\(537\) | −1.34125 | + | 20.7707i | −0.0578790 | + | 0.896323i | ||||
\(538\) | − | 4.10422i | − | 0.176946i | ||||||
\(539\) | −7.33790 | − | 14.3840i | −0.316066 | − | 0.619564i | ||||
\(540\) | −5.09922 | − | 0.998953i | −0.219436 | − | 0.0429881i | ||||
\(541\) | 4.59255 | − | 7.95454i | 0.197449 | − | 0.341992i | −0.750251 | − | 0.661153i | \(-0.770068\pi\) |
0.947701 | + | 0.319160i | \(0.103401\pi\) | |||||||
\(542\) | −4.53838 | − | 7.86071i | −0.194940 | − | 0.337646i | ||||
\(543\) | 13.7279 | + | 9.15351i | 0.589119 | + | 0.392815i | ||||
\(544\) | 5.45795 | + | 3.15115i | 0.234008 | + | 0.135104i | ||||
\(545\) | −6.66311 | −0.285416 | ||||||||
\(546\) | 21.5099 | + | 7.90584i | 0.920537 | + | 0.338339i | ||||
\(547\) | −5.21319 | −0.222900 | −0.111450 | − | 0.993770i | \(-0.535550\pi\) | ||||
−0.111450 | + | 0.993770i | \(0.535550\pi\) | |||||||
\(548\) | 1.07477 | + | 0.620520i | 0.0459120 | + | 0.0265073i | ||||
\(549\) | −2.30871 | + | 17.8019i | −0.0985332 | + | 0.759769i | ||||
\(550\) | −1.15340 | − | 1.99775i | −0.0491812 | − | 0.0851843i | ||||
\(551\) | 14.4921 | − | 25.1011i | 0.617386 | − | 1.06934i | ||||
\(552\) | −4.89136 | − | 9.89460i | −0.208190 | − | 0.421142i | ||||
\(553\) | −1.58208 | − | 6.58275i | −0.0672770 | − | 0.279927i | ||||
\(554\) | − | 0.216476i | − | 0.00919717i | ||||||
\(555\) | −11.9424 | − | 0.771166i | −0.506926 | − | 0.0327342i | ||||
\(556\) | 10.8551 | − | 6.26718i | 0.460358 | − | 0.265788i | ||||
\(557\) | 22.3550 | − | 12.9066i | 0.947210 | − | 0.546872i | 0.0549970 | − | 0.998487i | \(-0.482485\pi\) |
0.892213 | + | 0.451614i | \(0.149152\pi\) | |||||||
\(558\) | 5.05366 | + | 12.1343i | 0.213938 | + | 0.513685i | ||||
\(559\) | 12.7661i | 0.539947i | ||||||||
\(560\) | 2.53698 | + | 0.750813i | 0.107207 | + | 0.0317276i | ||||
\(561\) | 22.5732 | − | 11.1590i | 0.953042 | − | 0.471133i | ||||
\(562\) | −9.42488 | + | 16.3244i | −0.397565 | + | 0.688602i | ||||
\(563\) | 18.7468 | + | 32.4704i | 0.790084 | + | 1.36847i | 0.925914 | + | 0.377733i | \(0.123296\pi\) |
−0.135831 | + | 0.990732i | \(0.543370\pi\) | |||||||
\(564\) | 1.59203 | − | 2.38762i | 0.0670364 | − | 0.100537i | ||||
\(565\) | 3.85818 | + | 2.22752i | 0.162315 | + | 0.0937126i | ||||
\(566\) | −1.99832 | −0.0839956 | ||||||||
\(567\) | 0.525554 | − | 23.8060i | 0.0220712 | − | 0.999756i | ||||
\(568\) | −2.85910 | −0.119965 | ||||||||
\(569\) | −35.0352 | − | 20.2276i | −1.46875 | − | 0.847985i | −0.469367 | − | 0.883003i | \(-0.655518\pi\) |
−0.999387 | + | 0.0350177i | \(0.988851\pi\) | |||||||
\(570\) | 7.26157 | − | 10.8905i | 0.304154 | − | 0.456151i | ||||
\(571\) | 14.5551 | + | 25.2101i | 0.609111 | + | 1.05501i | 0.991387 | + | 0.130963i | \(0.0418070\pi\) |
−0.382276 | + | 0.924048i | \(0.624860\pi\) | |||||||
\(572\) | −5.76797 | + | 9.99042i | −0.241171 | + | 0.417720i | ||||
\(573\) | −7.71954 | + | 3.81613i | −0.322488 | + | 0.159421i | ||||
\(574\) | −25.1943 | + | 6.05514i | −1.05159 | + | 0.252737i | ||||
\(575\) | − | 6.37256i | − | 0.265754i | ||||||
\(576\) | 1.15340 | + | 2.76942i | 0.0480583 | + | 0.115392i | ||||
\(577\) | −13.1423 | + | 7.58769i | −0.547120 | + | 0.315880i | −0.747959 | − | 0.663744i | \(-0.768966\pi\) |
0.200840 | + | 0.979624i | \(0.435633\pi\) | |||||||
\(578\) | −19.6752 | + | 11.3595i | −0.818380 | + | 0.472492i | ||||
\(579\) | 10.4281 | + | 0.673383i | 0.433377 | + | 0.0279848i | ||||
\(580\) | 3.83533i | 0.159254i | ||||||||
\(581\) | 3.52550 | − | 3.34722i | 0.146262 | − | 0.138866i | ||||
\(582\) | 3.54403 | + | 7.16912i | 0.146905 | + | 0.297169i | ||||
\(583\) | −3.75176 | + | 6.49824i | −0.155382 | + | 0.269130i | ||||
\(584\) | −1.84089 | − | 3.18851i | −0.0761764 | − | 0.131941i | ||||
\(585\) | −1.92950 | + | 14.8779i | −0.0797748 | + | 0.615127i | ||||
\(586\) | 8.03773 | + | 4.64059i | 0.332036 | + | 0.191701i | ||||
\(587\) | −3.22807 | −0.133237 | −0.0666183 | − | 0.997779i | \(-0.521221\pi\) | ||||
−0.0666183 | + | 0.997779i | \(0.521221\pi\) | |||||||
\(588\) | −1.40754 | + | 12.0424i | −0.0580461 | + | 0.496619i | ||||
\(589\) | −33.1120 | −1.36436 | ||||||||
\(590\) | 8.60089 | + | 4.96573i | 0.354093 | + | 0.204436i | ||||
\(591\) | −20.4840 | − | 13.6584i | −0.842599 | − | 0.561831i | ||||
\(592\) | 3.45465 | + | 5.98363i | 0.141985 | + | 0.245926i | ||||
\(593\) | 21.8653 | − | 37.8717i | 0.897899 | − | 1.55521i | 0.0677234 | − | 0.997704i | \(-0.478426\pi\) |
0.830175 | − | 0.557502i | \(-0.188240\pi\) | |||||||
\(594\) | 11.7629 | + | 2.30439i | 0.482637 | + | 0.0945501i | ||||
\(595\) | −12.0923 | + | 11.4808i | −0.495736 | + | 0.470667i | ||||
\(596\) | 15.5951i | 0.638802i | ||||||||
\(597\) | −0.251227 | + | 3.89053i | −0.0102820 | + | 0.159229i | ||||
\(598\) | −27.5986 | + | 15.9341i | −1.12859 | + | 0.651593i | ||||
\(599\) | 6.96777 | − | 4.02284i | 0.284695 | − | 0.164369i | −0.350852 | − | 0.936431i | \(-0.614108\pi\) |
0.635547 | + | 0.772062i | \(0.280775\pi\) | |||||||
\(600\) | −0.111613 | + | 1.72845i | −0.00455657 | + | 0.0705637i | ||||
\(601\) | 8.38546i | 0.342050i | 0.985267 | + | 0.171025i | \(0.0547079\pi\) | ||||
−0.985267 | + | 0.171025i | \(0.945292\pi\) | |||||||
\(602\) | −6.56703 | + | 1.57830i | −0.267652 | + | 0.0643269i | ||||
\(603\) | 5.04090 | − | 6.59576i | 0.205281 | − | 0.268600i | ||||
\(604\) | 1.51958 | − | 2.63198i | 0.0618306 | − | 0.107094i | ||||
\(605\) | −2.83934 | − | 4.91787i | −0.115435 | − | 0.199940i | ||||
\(606\) | 16.3044 | + | 10.8715i | 0.662321 | + | 0.441624i | ||||
\(607\) | 14.6650 | + | 8.46682i | 0.595232 | + | 0.343658i | 0.767164 | − | 0.641451i | \(-0.221667\pi\) |
−0.171931 | + | 0.985109i | \(0.555001\pi\) | |||||||
\(608\) | −7.55717 | −0.306484 | ||||||||
\(609\) | −17.3182 | + | 2.99740i | −0.701770 | + | 0.121461i | ||||
\(610\) | 5.98368 | 0.242272 | ||||||||
\(611\) | −7.17550 | − | 4.14278i | −0.290290 | − | 0.167599i | ||||
\(612\) | −18.7499 | − | 2.43164i | −0.757919 | − | 0.0982933i | ||||
\(613\) | −16.9432 | − | 29.3464i | −0.684328 | − | 1.18529i | −0.973647 | − | 0.228058i | \(-0.926762\pi\) |
0.289319 | − | 0.957233i | \(-0.406571\pi\) | |||||||
\(614\) | −13.4641 | + | 23.3205i | −0.543366 | + | 0.941138i | ||||
\(615\) | −7.51732 | − | 15.2066i | −0.303128 | − | 0.613189i | ||||
\(616\) | −5.85231 | − | 1.73198i | −0.235796 | − | 0.0697833i | ||||
\(617\) | − | 37.5359i | − | 1.51114i | −0.655068 | − | 0.755570i | \(-0.727360\pi\) | ||
0.655068 | − | 0.755570i | \(-0.272640\pi\) | |||||||
\(618\) | −12.7284 | − | 0.821924i | −0.512013 | − | 0.0330626i | ||||
\(619\) | 14.6497 | − | 8.45802i | 0.588822 | − | 0.339957i | −0.175809 | − | 0.984424i | \(-0.556254\pi\) |
0.764632 | + | 0.644468i | \(0.222921\pi\) | |||||||
\(620\) | 3.79452 | − | 2.19077i | 0.152392 | − | 0.0879833i | ||||
\(621\) | 24.9587 | + | 21.7606i | 1.00156 | + | 0.873222i | ||||
\(622\) | 2.82130i | 0.113124i | ||||||||
\(623\) | −3.64021 | − | 15.1462i | −0.145842 | − | 0.606820i | ||||
\(624\) | 7.76475 | − | 3.83848i | 0.310839 | − | 0.153662i | ||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | −5.72135 | − | 9.90967i | −0.228671 | − | 0.396070i | ||||
\(627\) | −16.7510 | + | 25.1221i | −0.668971 | + | 1.00328i | ||||
\(628\) | 13.7050 | + | 7.91260i | 0.546890 | + | 0.315747i | ||||
\(629\) | −43.5445 | −1.73623 | ||||||||
\(630\) | −7.89195 | + | 0.846843i | −0.314423 | + | 0.0337390i | ||||
\(631\) | −29.1879 | −1.16195 | −0.580977 | − | 0.813920i | \(-0.697329\pi\) | ||||
−0.580977 | + | 0.813920i | \(0.697329\pi\) | |||||||
\(632\) | −2.21607 | − | 1.27945i | −0.0881504 | − | 0.0508937i | ||||
\(633\) | −26.5236 | + | 39.7785i | −1.05422 | + | 1.58105i | ||||
\(634\) | −4.65491 | − | 8.06254i | −0.184870 | − | 0.320204i | ||||
\(635\) | 0.918471 | − | 1.59084i | 0.0364484 | − | 0.0631305i | ||||
\(636\) | 5.05056 | − | 2.49673i | 0.200268 | − | 0.0990016i | ||||
\(637\) | 34.9588 | + | 1.81495i | 1.38512 | + | 0.0719108i | ||||
\(638\) | − | 8.84735i | − | 0.350270i | ||||||
\(639\) | 7.91803 | − | 3.29768i | 0.313232 | − | 0.130454i | ||||
\(640\) | 0.866025 | − | 0.500000i | 0.0342327 | − | 0.0197642i | ||||
\(641\) | −3.95871 | + | 2.28556i | −0.156360 | + | 0.0902743i | −0.576138 | − | 0.817352i | \(-0.695441\pi\) |
0.419779 | + | 0.907627i | \(0.362108\pi\) | |||||||
\(642\) | 14.5514 | + | 0.939639i | 0.574297 | + | 0.0370846i | ||||
\(643\) | 24.0758i | 0.949457i | 0.880132 | + | 0.474728i | \(0.157454\pi\) | ||||
−0.880132 | + | 0.474728i | \(0.842546\pi\) | |||||||
\(644\) | −11.6088 | − | 12.2271i | −0.457451 | − | 0.481816i | ||||
\(645\) | −1.95943 | − | 3.96368i | −0.0771524 | − | 0.156070i | ||||
\(646\) | 23.8138 | − | 41.2467i | 0.936940 | − | 1.62283i | ||||
\(647\) | −8.71205 | − | 15.0897i | −0.342506 | − | 0.593238i | 0.642391 | − | 0.766377i | \(-0.277942\pi\) |
−0.984897 | + | 0.173139i | \(0.944609\pi\) | |||||||
\(648\) | −6.38849 | − | 6.33934i | −0.250964 | − | 0.249033i | ||||
\(649\) | −19.8405 | − | 11.4549i | −0.778809 | − | 0.449646i | ||||
\(650\) | 5.00084 | 0.196149 | ||||||||
\(651\) | 12.8578 | + | 15.4218i | 0.503936 | + | 0.604428i | ||||
\(652\) | 8.61682 | 0.337461 | ||||||||
\(653\) | −32.8146 | − | 18.9455i | −1.28414 | − | 0.741396i | −0.306534 | − | 0.951860i | \(-0.599169\pi\) |
−0.977602 | + | 0.210464i | \(0.932503\pi\) | |||||||
\(654\) | −9.60205 | − | 6.40249i | −0.375470 | − | 0.250357i | ||||
\(655\) | −2.76942 | − | 4.79677i | −0.108210 | − | 0.187425i | ||||
\(656\) | −4.89686 | + | 8.48160i | −0.191190 | + | 0.331151i | ||||
\(657\) | 8.77580 | + | 6.70703i | 0.342377 | + | 0.261666i | ||||
\(658\) | 1.24397 | − | 4.20336i | 0.0484950 | − | 0.163864i | ||||
\(659\) | − | 24.7262i | − | 0.963197i | −0.876392 | − | 0.481599i | \(-0.840056\pi\) | ||
0.876392 | − | 0.481599i | \(-0.159944\pi\) | |||||||
\(660\) | 0.257468 | − | 3.98719i | 0.0100219 | − | 0.155201i | ||||
\(661\) | −37.8348 | + | 21.8439i | −1.47160 | + | 0.849631i | −0.999491 | − | 0.0319070i | \(-0.989842\pi\) |
−0.472113 | + | 0.881538i | \(0.656509\pi\) | |||||||
\(662\) | −15.8448 | + | 9.14801i | −0.615826 | + | 0.355547i | ||||
\(663\) | −3.51767 | + | 54.4752i | −0.136615 | + | 2.11564i | ||||
\(664\) | − | 1.83743i | − | 0.0713060i | ||||||
\(665\) | 5.67402 | − | 19.1724i | 0.220029 | − | 0.743474i | ||||
\(666\) | −16.4689 | − | 12.5866i | −0.638156 | − | 0.487720i | ||||
\(667\) | 12.2205 | − | 21.1664i | 0.473178 | − | 0.819568i | ||||
\(668\) | −4.32474 | − | 7.49067i | −0.167329 | − | 0.289823i | ||||
\(669\) | 33.2567 | + | 22.1750i | 1.28578 | + | 0.857334i | ||||
\(670\) | −2.39643 | − | 1.38358i | −0.0925823 | − | 0.0534524i | ||||
\(671\) | −13.8031 | −0.532865 | ||||||||
\(672\) | 2.93454 | + | 3.51973i | 0.113202 | + | 0.135776i | ||||
\(673\) | 34.1588 | 1.31673 | 0.658363 | − | 0.752701i | \(-0.271249\pi\) | ||||
0.658363 | + | 0.752701i | \(0.271249\pi\) | |||||||
\(674\) | 6.79410 | + | 3.92258i | 0.261699 | + | 0.151092i | ||||
\(675\) | −1.68449 | − | 4.91553i | −0.0648362 | − | 0.189199i | ||||
\(676\) | −6.00420 | − | 10.3996i | −0.230931 | − | 0.399984i | ||||
\(677\) | −6.56630 | + | 11.3732i | −0.252364 | + | 0.437106i | −0.964176 | − | 0.265263i | \(-0.914541\pi\) |
0.711813 | + | 0.702369i | \(0.247875\pi\) | |||||||
\(678\) | 3.41954 | + | 6.91730i | 0.131327 | + | 0.265657i | ||||
\(679\) | 8.41113 | + | 8.85914i | 0.322790 | + | 0.339983i | ||||
\(680\) | 6.30230i | 0.241682i | ||||||||
\(681\) | 34.6296 | + | 2.23617i | 1.32701 | + | 0.0856902i | ||||
\(682\) | −8.75320 | + | 5.05366i | −0.335177 | + | 0.193515i | ||||
\(683\) | 39.7352 | − | 22.9411i | 1.52043 | − | 0.877818i | 0.520716 | − | 0.853730i | \(-0.325665\pi\) |
0.999710 | − | 0.0240882i | \(-0.00766825\pi\) | |||||||
\(684\) | 20.9290 | − | 8.71645i | 0.800239 | − | 0.333282i | ||||
\(685\) | 1.24104i | 0.0474177i | ||||||||
\(686\) | 3.38843 | + | 18.2077i | 0.129371 | + | 0.695171i | ||||
\(687\) | −44.6628 | + | 22.0789i | −1.70399 | + | 0.842363i | ||||
\(688\) | −1.27639 | + | 2.21077i | −0.0486620 | + | 0.0842850i | ||||
\(689\) | −8.13333 | − | 14.0873i | −0.309855 | − | 0.536685i | ||||
\(690\) | 6.12330 | − | 9.18334i | 0.233110 | − | 0.349604i | ||||
\(691\) | −15.2114 | − | 8.78233i | −0.578671 | − | 0.334096i | 0.181934 | − | 0.983311i | \(-0.441764\pi\) |
−0.760605 | + | 0.649215i | \(0.775098\pi\) | |||||||
\(692\) | 17.9315 | 0.681652 | ||||||||
\(693\) | 18.2052 | − | 1.95350i | 0.691557 | − | 0.0742073i | ||||
\(694\) | −0.232294 | −0.00881775 | ||||||||
\(695\) | 10.8551 | + | 6.26718i | 0.411757 | + | 0.237728i | ||||
\(696\) | −3.68532 | + | 5.52701i | −0.139692 | + | 0.209501i | ||||
\(697\) | −30.8614 | − | 53.4536i | −1.16896 | − | 2.02470i | ||||
\(698\) | −5.78426 | + | 10.0186i | −0.218938 | + | 0.379211i | ||||
\(699\) | 39.9220 | − | 19.7353i | 1.50999 | − | 0.746458i | ||||
\(700\) | 0.618268 | + | 2.57250i | 0.0233683 | + | 0.0972313i | ||||
\(701\) | 39.2501i | 1.48246i | 0.671253 | + | 0.741228i | \(0.265756\pi\) | ||||
−0.671253 | + | 0.741228i | \(0.734244\pi\) | |||||||
\(702\) | −17.0765 | + | 19.5862i | −0.644512 | + | 0.739234i | ||||
\(703\) | 45.2193 | − | 26.1074i | 1.70548 | − | 0.984659i | ||||
\(704\) | −1.99775 | + | 1.15340i | −0.0752930 | + | 0.0434704i | ||||
\(705\) | 2.86375 | + | 0.184924i | 0.107855 | + | 0.00696463i | ||||
\(706\) | 34.7075i | 1.30623i | ||||||||
\(707\) | 28.7035 | + | 8.49472i | 1.07951 | + | 0.319477i | ||||
\(708\) | 7.62305 | + | 15.4205i | 0.286492 | + | 0.579536i | ||||
\(709\) | 23.8340 | − | 41.2817i | 0.895105 | − | 1.55037i | 0.0614314 | − | 0.998111i | \(-0.480433\pi\) |
0.833674 | − | 0.552257i | \(-0.186233\pi\) | |||||||
\(710\) | −1.42955 | − | 2.47605i | −0.0536500 | − | 0.0929245i | ||||
\(711\) | 7.61293 | + | 0.987309i | 0.285507 | + | 0.0370270i | ||||
\(712\) | −5.09894 | − | 2.94387i | −0.191091 | − | 0.110326i | ||||
\(713\) | −27.9216 | −1.04567 | ||||||||
\(714\) | −28.4577 | + | 4.92539i | −1.06500 | + | 0.184328i | ||||
\(715\) | −11.5359 | −0.431420 | ||||||||
\(716\) | 10.4070 | + | 6.00848i | 0.388928 | + | 0.224547i | ||||
\(717\) | −15.4513 | − | 10.3026i | −0.577039 | − | 0.384759i | ||||
\(718\) | 8.76612 | + | 15.1834i | 0.327149 | + | 0.566638i | ||||
\(719\) | −16.7107 | + | 28.9438i | −0.623205 | + | 1.07942i | 0.365680 | + | 0.930740i | \(0.380836\pi\) |
−0.988885 | + | 0.148682i | \(0.952497\pi\) | |||||||
\(720\) | −1.82168 | + | 2.38358i | −0.0678902 | + | 0.0888309i | ||||
\(721\) | −18.9441 | + | 4.55297i | −0.705513 | + | 0.169561i | ||||
\(722\) | 38.1109i | 1.41834i | ||||||||
\(723\) | −0.132222 | + | 2.04761i | −0.00491739 | + | 0.0761514i | ||||
\(724\) | 8.24987 | − | 4.76306i | 0.306604 | − | 0.177018i | ||||
\(725\) | −3.32150 | + | 1.91767i | −0.123357 | + | 0.0712204i | ||||
\(726\) | 0.633812 | − | 9.81530i | 0.0235230 | − | 0.364280i | ||||
\(727\) | 31.9845i | 1.18624i | 0.805115 | + | 0.593119i | \(0.202104\pi\) | ||||
−0.805115 | + | 0.593119i | \(0.797896\pi\) | |||||||
\(728\) | 9.59518 | − | 9.10996i | 0.355621 | − | 0.337637i | ||||
\(729\) | 25.0042 | + | 10.1878i | 0.926081 | + | 0.377325i | ||||
\(730\) | 1.84089 | − | 3.18851i | 0.0681342 | − | 0.118012i | ||||
\(731\) | −8.04420 | − | 13.9330i | −0.297525 | − | 0.515329i | ||||
\(732\) | 8.62293 | + | 5.74962i | 0.318713 | + | 0.212512i | ||||
\(733\) | 33.9483 | + | 19.6001i | 1.25391 | + | 0.723945i | 0.971884 | − | 0.235461i | \(-0.0756601\pi\) |
0.282026 | + | 0.959407i | \(0.408993\pi\) | |||||||
\(734\) | −10.0402 | −0.370590 | ||||||||
\(735\) | −11.1328 | + | 4.80222i | −0.410639 | + | 0.177133i | ||||
\(736\) | −6.37256 | −0.234896 | ||||||||
\(737\) | 5.52810 | + | 3.19165i | 0.203630 | + | 0.117566i | ||||
\(738\) | 3.77875 | − | 29.1371i | 0.139098 | − | 1.07255i | ||||
\(739\) | 16.8814 | + | 29.2394i | 0.620992 | + | 1.07559i | 0.989301 | + | 0.145886i | \(0.0466033\pi\) |
−0.368310 | + | 0.929703i | \(0.620063\pi\) | |||||||
\(740\) | −3.45465 | + | 5.98363i | −0.126995 | + | 0.219963i | ||||
\(741\) | −29.0080 | − | 58.6796i | −1.06564 | − | 2.15565i | ||||
\(742\) | 6.24116 | − | 5.92555i | 0.229120 | − | 0.217534i | ||||
\(743\) | − | 14.3933i | − | 0.528038i | −0.964517 | − | 0.264019i | \(-0.914952\pi\) | ||
0.964517 | − | 0.264019i | \(-0.0850482\pi\) | |||||||
\(744\) | 7.57326 | + | 0.489035i | 0.277649 | + | 0.0179289i | ||||
\(745\) | −13.5058 | + | 7.79757i | −0.494814 | + | 0.285681i | ||||
\(746\) | 0.00417483 | − | 0.00241034i | 0.000152851 | − | 8.82487e-5i | ||||
\(747\) | 2.11929 | + | 5.08860i | 0.0775408 | + | 0.186182i | ||||
\(748\) | − | 14.5381i | − | 0.531567i | ||||||
\(749\) | 21.6572 | − | 5.20504i | 0.791336 | − | 0.190188i | ||||
\(750\) | −1.55269 | + | 0.767566i | −0.0566962 | + | 0.0280275i | ||||
\(751\) | −8.92040 | + | 15.4506i | −0.325510 | + | 0.563800i | −0.981615 | − | 0.190869i | \(-0.938869\pi\) |
0.656105 | + | 0.754669i | \(0.272203\pi\) | |||||||
\(752\) | −0.828416 | − | 1.43486i | −0.0302092 | − | 0.0523239i | ||||
\(753\) | 13.8069 | − | 20.7067i | 0.503150 | − | 0.754594i | ||||
\(754\) | 16.6103 | + | 9.58995i | 0.604911 | + | 0.349245i | ||||
\(755\) | 3.03915 | 0.110606 | ||||||||
\(756\) | −12.1866 | − | 6.36289i | −0.443223 | − | 0.231416i | ||||
\(757\) | −1.90604 | −0.0692760 | −0.0346380 | − | 0.999400i | \(-0.511028\pi\) | ||||
−0.0346380 | + | 0.999400i | \(0.511028\pi\) | |||||||
\(758\) | 16.1576 | + | 9.32860i | 0.586871 | + | 0.338830i | ||||
\(759\) | −14.1252 | + | 21.1841i | −0.512713 | + | 0.768936i | ||||
\(760\) | −3.77859 | − | 6.54470i | −0.137064 | − | 0.237401i | ||||
\(761\) | −14.1364 | + | 24.4850i | −0.512445 | + | 0.887581i | 0.487451 | + | 0.873150i | \(0.337927\pi\) |
−0.999896 | + | 0.0144304i | \(0.995407\pi\) | |||||||
\(762\) | 2.85220 | − | 1.40997i | 0.103324 | − | 0.0510780i | ||||
\(763\) | −16.9042 | − | 5.00275i | −0.611973 | − | 0.181112i | ||||
\(764\) | 4.97173i | 0.179871i | ||||||||
\(765\) | −7.26907 | − | 17.4537i | −0.262814 | − | 0.631039i | ||||
\(766\) | −16.3214 | + | 9.42316i | −0.589716 | + | 0.340473i | ||||
\(767\) | 43.0117 | − | 24.8328i | 1.55306 | − | 0.896661i | ||||
\(768\) | 1.72845 | + | 0.111613i | 0.0623701 | + | 0.00402748i | ||||
\(769\) | − | 1.43146i | − | 0.0516197i | −0.999667 | − | 0.0258098i | \(-0.991784\pi\) | ||
0.999667 | − | 0.0258098i | \(-0.00821644\pi\) | |||||||
\(770\) | −1.42622 | − | 5.93424i | −0.0513975 | − | 0.213855i | ||||
\(771\) | 12.6925 | + | 25.6753i | 0.457109 | + | 0.924675i | ||||
\(772\) | 3.01660 | − | 5.22491i | 0.108570 | − | 0.188049i | ||||
\(773\) | −17.4088 | − | 30.1528i | −0.626149 | − | 1.08452i | −0.988317 | − | 0.152410i | \(-0.951297\pi\) |
0.362168 | − | 0.932113i | \(-0.382037\pi\) | |||||||
\(774\) | 0.984951 | − | 7.59475i | 0.0354033 | − | 0.272987i | ||||
\(775\) | 3.79452 | + | 2.19077i | 0.136303 | + | 0.0786946i | ||||
\(776\) | 4.61723 | 0.165749 | ||||||||
\(777\) | −29.7186 | − | 10.9229i | −1.06615 | − | 0.391858i | ||||
\(778\) | −10.8601 | −0.389352 | ||||||||
\(779\) | 64.0969 | + | 37.0064i | 2.29651 | + | 1.32589i | ||||
\(780\) | 7.20659 | + | 4.80523i | 0.258037 | + | 0.172055i | ||||
\(781\) | 3.29768 | + | 5.71175i | 0.118000 | + | 0.204383i | ||||
\(782\) | 20.0809 | − | 34.7811i | 0.718091 | − | 1.24377i | ||||
\(783\) | 3.83132 | − | 19.5572i | 0.136920 | − | 0.698918i | ||||
\(784\) | 5.87256 | + | 3.80960i | 0.209734 | + | 0.136057i | ||||
\(785\) | 15.8252i | 0.564826i | ||||||||
\(786\) | 0.618204 | − | 9.57360i | 0.0220506 | − | 0.341479i | ||||
\(787\) | −43.0486 | + | 24.8541i | −1.53452 | + | 0.885953i | −0.535370 | + | 0.844617i | \(0.679828\pi\) |
−0.999145 | + | 0.0413355i | \(0.986839\pi\) | |||||||
\(788\) | −12.3100 | + | 7.10719i | −0.438526 | + | 0.253183i | ||||
\(789\) | 3.45330 | − | 53.4782i | 0.122941 | − | 1.90388i | ||||
\(790\) | − | 2.55889i | − | 0.0910414i | ||||||
\(791\) | 8.11569 | + | 8.54796i | 0.288561 | + | 0.303931i | ||||
\(792\) | 4.20226 | − | 5.49845i | 0.149321 | − | 0.195379i | ||||
\(793\) | 14.9617 | − | 25.9144i | 0.531306 | − | 0.920249i | ||||
\(794\) | −13.5204 | − | 23.4180i | −0.479822 | − | 0.831075i | ||||
\(795\) | 4.68751 | + | 3.12555i | 0.166249 | + | 0.110852i | ||||
\(796\) | 1.94932 | + | 1.12544i | 0.0690917 | + | 0.0398901i | ||||
\(797\) | 8.43295 | 0.298710 | 0.149355 | − | 0.988784i | \(-0.452280\pi\) | ||||
0.149355 | + | 0.988784i | \(0.452280\pi\) | |||||||
\(798\) | 26.5992 | − | 22.1768i | 0.941601 | − | 0.785051i | ||||
\(799\) | 10.4419 | 0.369406 | ||||||||
\(800\) | 0.866025 | + | 0.500000i | 0.0306186 | + | 0.0176777i | ||||
\(801\) | 17.5165 | + | 2.27169i | 0.618917 | + | 0.0802664i | ||||
\(802\) | −12.2627 | − | 21.2396i | −0.433012 | − | 0.749998i | ||||
\(803\) | −4.24656 | + | 7.35525i | −0.149858 | + | 0.259561i | ||||
\(804\) | −2.12398 | − | 4.29655i | −0.0749070 | − | 0.151527i | ||||
\(805\) | 4.78460 | − | 16.1671i | 0.168635 | − | 0.569814i | ||||
\(806\) | − | 21.9113i | − | 0.771794i | ||||||
\(807\) | 7.09394 | + | 0.458083i | 0.249719 | + | 0.0161253i | ||||
\(808\) | 9.79825 | − | 5.65702i | 0.344701 | − | 0.199013i | ||||
\(809\) | −33.7531 | + | 19.4873i | −1.18669 | + | 0.685138i | −0.957554 | − | 0.288255i | \(-0.906925\pi\) |
−0.229141 | + | 0.973393i | \(0.573592\pi\) | |||||||
\(810\) | 2.29578 | − | 8.70226i | 0.0806655 | − | 0.305766i | ||||
\(811\) | − | 29.5668i | − | 1.03823i | −0.854704 | − | 0.519116i | \(-0.826261\pi\) | ||
0.854704 | − | 0.519116i | \(-0.173739\pi\) | |||||||
\(812\) | −2.87962 | + | 9.73018i | −0.101055 | + | 0.341462i | ||||
\(813\) | 14.0934 | − | 6.96702i | 0.494277 | − | 0.244344i | ||||
\(814\) | 7.96919 | − | 13.8030i | 0.279320 | − | 0.483796i | ||||
\(815\) | 4.30841 | + | 7.46238i | 0.150917 | + | 0.261396i | ||||
\(816\) | −6.05578 | + | 9.08209i | −0.211995 | + | 0.317937i | ||||
\(817\) | 16.7072 | + | 9.64591i | 0.584511 | + | 0.337468i | ||||
\(818\) | 5.40347 | 0.188928 | ||||||||
\(819\) | −16.0656 | + | 36.2964i | −0.561379 | + | 1.26830i | ||||
\(820\) | −9.79371 | −0.342011 | ||||||||
\(821\) | −29.1479 | − | 16.8285i | −1.01727 | − | 0.587320i | −0.103956 | − | 0.994582i | \(-0.533150\pi\) |
−0.913311 | + | 0.407262i | \(0.866484\pi\) | |||||||
\(822\) | −1.19250 | + | 1.78843i | −0.0415931 | + | 0.0623788i | ||||
\(823\) | 6.27024 | + | 10.8604i | 0.218567 | + | 0.378569i | 0.954370 | − | 0.298627i | \(-0.0965285\pi\) |
−0.735803 | + | 0.677195i | \(0.763195\pi\) | |||||||
\(824\) | −3.68203 | + | 6.37747i | −0.128270 | + | 0.222170i | ||||
\(825\) | 3.58174 | − | 1.77062i | 0.124700 | − | 0.0616451i | ||||
\(826\) | 18.0920 | + | 19.0556i | 0.629501 | + | 0.663030i | ||||
\(827\) | 15.6875i | 0.545506i | 0.962084 | + | 0.272753i | \(0.0879342\pi\) | ||||
−0.962084 | + | 0.272753i | \(0.912066\pi\) | |||||||
\(828\) | 17.6483 | − | 7.35011i | 0.613320 | − | 0.255434i | ||||
\(829\) | −4.91198 | + | 2.83593i | −0.170600 | + | 0.0984959i | −0.582869 | − | 0.812566i | \(-0.698070\pi\) |
0.412269 | + | 0.911062i | \(0.364736\pi\) | |||||||
\(830\) | 1.59126 | − | 0.918714i | 0.0552334 | − | 0.0318890i | ||||
\(831\) | 0.374168 | + | 0.0241614i | 0.0129797 | + | 0.000838151i | ||||
\(832\) | − | 5.00084i | − | 0.173373i | ||||||
\(833\) | −39.2979 | + | 20.0475i | −1.36159 | + | 0.694606i | ||||
\(834\) | 9.62095 | + | 19.4620i | 0.333146 | + | 0.673913i | ||||
\(835\) | 4.32474 | − | 7.49067i | 0.149664 | − | 0.259225i | ||||
\(836\) | 8.71645 | + | 15.0973i | 0.301465 | + | 0.522152i | ||||
\(837\) | −21.5376 | + | 7.38066i | −0.744447 | + | 0.255113i | ||||
\(838\) | −24.5024 | − | 14.1465i | −0.846422 | − | 0.488682i | ||||
\(839\) | −14.5217 | −0.501346 | −0.250673 | − | 0.968072i | \(-0.580652\pi\) | ||||
−0.250673 | + | 0.968072i | \(0.580652\pi\) | |||||||
\(840\) | −1.58090 | + | 4.30125i | −0.0545463 | + | 0.148407i | ||||
\(841\) | 14.2902 | 0.492766 | ||||||||
\(842\) | −21.7967 | − | 12.5843i | −0.751165 | − | 0.433685i | ||||
\(843\) | −27.1639 | − | 18.1125i | −0.935576 | − | 0.623826i | ||||
\(844\) | 13.8017 | + | 23.9052i | 0.475073 | + | 0.822851i | ||||
\(845\) | 6.00420 | − | 10.3996i | 0.206551 | − | 0.357757i | ||||
\(846\) | 3.94920 | + | 3.01823i | 0.135776 | + | 0.103769i | ||||
\(847\) | −3.51094 | − | 14.6084i | −0.120637 | − | 0.501949i | ||||
\(848\) | − | 3.25278i | − | 0.111701i | ||||||
\(849\) | 0.223038 | − | 3.45400i | 0.00765464 | − | 0.118541i | ||||
\(850\) | −5.45795 | + | 3.15115i | −0.187206 | + | 0.108083i | ||||
\(851\) | 38.1310 | − | 22.0150i | 1.30712 | − | 0.754663i | ||||
\(852\) | 0.319112 | − | 4.94181i | 0.0109326 | − | 0.169304i | ||||
\(853\) | 3.66698i | 0.125555i | 0.998028 | + | 0.0627775i | \(0.0199958\pi\) | ||||
−0.998028 | + | 0.0627775i | \(0.980004\pi\) | |||||||
\(854\) | 15.1805 | + | 4.49262i | 0.519465 | + | 0.153734i | ||||
\(855\) | 18.0131 | + | 13.7668i | 0.616037 | + | 0.470814i | ||||
\(856\) | 4.20937 | − | 7.29084i | 0.143873 | − | 0.249196i | ||||
\(857\) | 5.78149 | + | 10.0138i | 0.197492 | + | 0.342066i | 0.947715 | − | 0.319119i | \(-0.103387\pi\) |
−0.750223 | + | 0.661185i | \(0.770054\pi\) | |||||||
\(858\) | −16.6242 | − | 11.0847i | −0.567540 | − | 0.378426i | ||||
\(859\) | −12.9614 | − | 7.48325i | −0.442236 | − | 0.255325i | 0.262310 | − | 0.964984i | \(-0.415516\pi\) |
−0.704546 | + | 0.709659i | \(0.748849\pi\) | |||||||
\(860\) | −2.55278 | −0.0870492 | ||||||||
\(861\) | −7.65401 | − | 44.2229i | −0.260848 | − | 1.50711i | ||||
\(862\) | −11.2182 | −0.382093 | ||||||||
\(863\) | 8.11706 | + | 4.68639i | 0.276308 | + | 0.159526i | 0.631751 | − | 0.775172i | \(-0.282337\pi\) |
−0.355443 | + | 0.934698i | \(0.615670\pi\) | |||||||
\(864\) | −4.91553 | + | 1.68449i | −0.167230 | + | 0.0573076i | ||||
\(865\) | 8.96573 | + | 15.5291i | 0.304844 | + | 0.528005i | ||||
\(866\) | 0.319796 | − | 0.553903i | 0.0108671 | − | 0.0188224i | ||||
\(867\) | −17.4383 | − | 35.2754i | −0.592235 | − | 1.19802i | ||||
\(868\) | 11.2715 | − | 2.70896i | 0.382579 | − | 0.0919482i | ||||
\(869\) | 5.90286i | 0.200241i | ||||||||
\(870\) | −6.62919 | − | 0.428072i | −0.224751 | − | 0.0145130i | ||||
\(871\) | −11.9842 | + | 6.91907i | −0.406069 | + | 0.234444i | ||||
\(872\) | −5.77043 | + | 3.33156i | −0.195411 | + | 0.112821i | ||||
\(873\) | −12.7870 | + | 5.32551i | −0.432775 | + | 0.180241i | ||||
\(874\) | 48.1585i | 1.62899i | ||||||||
\(875\) | −1.91871 | + | 1.82168i | −0.0648644 | + | 0.0615842i | ||||
\(876\) | 5.71664 | − | 2.82600i | 0.193148 | − | 0.0954818i | ||||
\(877\) | 7.81117 | − | 13.5293i | 0.263764 | − | 0.456853i | −0.703475 | − | 0.710720i | \(-0.748369\pi\) |
0.967239 | + | 0.253867i | \(0.0817025\pi\) | |||||||
\(878\) | −6.58174 | − | 11.3999i | −0.222123 | − | 0.384728i | ||||
\(879\) | −8.91814 | + | 13.3749i | −0.300801 | + | 0.451123i | ||||
\(880\) | −1.99775 | − | 1.15340i | −0.0673441 | − | 0.0388811i | ||||
\(881\) | 4.54709 | 0.153195 | 0.0765977 | − | 0.997062i | \(-0.475594\pi\) | ||||
0.0765977 | + | 0.997062i | \(0.475594\pi\) | |||||||
\(882\) | −20.6576 | − | 3.77695i | −0.695576 | − | 0.127177i | ||||
\(883\) | −48.8190 | −1.64289 | −0.821445 | − | 0.570288i | \(-0.806831\pi\) | ||||
−0.821445 | + | 0.570288i | \(0.806831\pi\) | |||||||
\(884\) | 27.2943 | + | 15.7584i | 0.918008 | + | 0.530012i | ||||
\(885\) | −9.54298 | + | 14.3120i | −0.320784 | + | 0.481092i | ||||
\(886\) | −12.9223 | − | 22.3821i | −0.434133 | − | 0.751941i | ||||
\(887\) | 3.64168 | − | 6.30758i | 0.122276 | − | 0.211788i | −0.798389 | − | 0.602142i | \(-0.794314\pi\) |
0.920665 | + | 0.390354i | \(0.127647\pi\) | |||||||
\(888\) | −10.7280 | + | 5.30334i | −0.360008 | + | 0.177969i | ||||
\(889\) | 3.52457 | − | 3.34633i | 0.118210 | − | 0.112232i | ||||
\(890\) | − | 5.88774i | − | 0.197358i | ||||||
\(891\) | −5.29591 | + | 20.0744i | −0.177420 | + | 0.672517i | ||||
\(892\) | 19.9858 | − | 11.5388i | 0.669176 | − | 0.386349i | ||||
\(893\) | −10.8435 | + | 6.26049i | −0.362863 | + | 0.209499i | ||||
\(894\) | −26.9554 | − | 1.74062i | −0.901525 | − | 0.0582149i | ||||
\(895\) | 12.0170i | 0.401683i | ||||||||
\(896\) | 2.57250 | − | 0.618268i | 0.0859411 | − | 0.0206549i | ||||
\(897\) | −24.4609 | − | 49.4813i | −0.816726 | − | 1.65213i | ||||
\(898\) | 14.1793 | − | 24.5593i | 0.473170 | − | 0.819554i | ||||
\(899\) | 8.40232 | + | 14.5532i | 0.280233 | + | 0.485378i | ||||
\(900\) | −2.97509 | − | 0.385834i | −0.0991695 | − | 0.0128611i | ||||
\(901\) | 17.7535 | + | 10.2500i | 0.591456 | + | 0.341477i | ||||
\(902\) | 22.5921 | 0.752236 | ||||||||
\(903\) | −1.99506 | − | 11.5269i | −0.0663914 | − | 0.383593i | ||||
\(904\) | 4.45505 | 0.148173 | ||||||||
\(905\) | 8.24987 | + | 4.76306i | 0.274235 | + | 0.158330i | ||||
\(906\) | 4.37965 | + | 2.92027i | 0.145504 | + | 0.0970196i | ||||
\(907\) | 13.4481 | + | 23.2928i | 0.446537 | + | 0.773425i | 0.998158 | − | 0.0606703i | \(-0.0193238\pi\) |
−0.551621 | + | 0.834095i | \(0.685990\pi\) | |||||||
\(908\) | 10.0175 | − | 17.3509i | 0.332444 | − | 0.575809i | ||||
\(909\) | −20.6106 | + | 26.9679i | −0.683611 | + | 0.894470i | ||||
\(910\) | 12.6870 | + | 3.75470i | 0.420571 | + | 0.124467i | ||||
\(911\) | − | 46.4059i | − | 1.53750i | −0.639552 | − | 0.768748i | \(-0.720880\pi\) | ||
0.639552 | − | 0.768748i | \(-0.279120\pi\) | |||||||
\(912\) | 0.843477 | − | 13.0622i | 0.0279303 | − | 0.432533i | ||||
\(913\) | −3.67072 | + | 2.11929i | −0.121483 | + | 0.0701383i | ||||
\(914\) | 25.2797 | − | 14.5953i | 0.836179 | − | 0.482768i | ||||
\(915\) | −0.667855 | + | 10.3425i | −0.0220786 | + | 0.341912i | ||||
\(916\) | 28.7648i | 0.950417i | ||||||||
\(917\) | −3.42448 | − | 14.2486i | −0.113086 | − | 0.470531i | ||||
\(918\) | 6.29570 | − | 32.1368i | 0.207789 | − | 1.06067i | ||||
\(919\) | 2.26073 | − | 3.91570i | 0.0745746 | − | 0.129167i | −0.826327 | − | 0.563191i | \(-0.809573\pi\) |
0.900901 | + | 0.434024i | \(0.142907\pi\) | |||||||
\(920\) | −3.18628 | − | 5.51880i | −0.105049 | − | 0.181949i | ||||
\(921\) | −38.8055 | − | 25.8749i | −1.27869 | − | 0.852606i | ||||
\(922\) | 26.9306 | + | 15.5484i | 0.886913 | + | 0.512060i | ||||
\(923\) | −14.2979 | −0.470621 | ||||||||
\(924\) | 3.64683 | − | 9.92212i | 0.119972 | − | 0.326414i | ||||
\(925\) | −6.90930 | −0.227176 | ||||||||
\(926\) | −29.0045 | − | 16.7457i | −0.953146 | − | 0.550299i | ||||
\(927\) | 2.84131 | − | 21.9087i | 0.0933209 | − | 0.719577i | ||||
\(928\) | 1.91767 | + | 3.32150i | 0.0629505 | + | 0.109033i | ||||
\(929\) | −8.30472 | + | 14.3842i | −0.272469 | + | 0.471930i | −0.969493 | − | 0.245117i | \(-0.921174\pi\) |
0.697025 | + | 0.717047i | \(0.254507\pi\) | |||||||
\(930\) | 3.36311 | + | 6.80316i | 0.110281 | + | 0.223084i | ||||
\(931\) | 28.7898 | − | 44.3800i | 0.943547 | − | 1.45449i | ||||
\(932\) | − | 25.7115i | − | 0.842209i | ||||||
\(933\) | −4.87647 | − | 0.314892i | −0.159648 | − | 0.0103091i | ||||
\(934\) | −12.8389 | + | 7.41254i | −0.420102 | + | 0.242546i | ||||
\(935\) | 12.5904 | − | 7.26907i | 0.411750 | − | 0.237724i | ||||
\(936\) | 5.76797 | + | 13.8494i | 0.188532 | + | 0.452682i | ||||
\(937\) | 20.5347i | 0.670839i | 0.942069 | + | 0.335419i | \(0.108878\pi\) | ||||
−0.942069 | + | 0.335419i | \(0.891122\pi\) | |||||||
\(938\) | −5.04090 | − | 5.30940i | −0.164591 | − | 0.173358i | ||||
\(939\) | 17.7670 | − | 8.78303i | 0.579803 | − | 0.286623i | ||||
\(940\) | 0.828416 | − | 1.43486i | 0.0270200 | − | 0.0467999i | ||||
\(941\) | 12.1992 | + | 21.1296i | 0.397682 | + | 0.688805i | 0.993439 | − | 0.114359i | \(-0.0364814\pi\) |
−0.595758 | + | 0.803164i | \(0.703148\pi\) | |||||||
\(942\) | −15.2062 | + | 22.8053i | −0.495445 | + | 0.743037i | ||||
\(943\) | 54.0495 | + | 31.2055i | 1.76009 | + | 1.01619i | ||||
\(944\) | 9.93145 | 0.323241 | ||||||||
\(945\) | −0.582885 | − | 13.7354i | −0.0189612 | − | 0.446811i | ||||
\(946\) | 5.88876 | 0.191460 | ||||||||
\(947\) | 16.5526 | + | 9.55667i | 0.537888 | + | 0.310550i | 0.744223 | − | 0.667932i | \(-0.232820\pi\) |
−0.206334 | + | 0.978482i | \(0.566153\pi\) | |||||||
\(948\) | 2.45880 | − | 3.68756i | 0.0798582 | − | 0.119766i | ||||
\(949\) | −9.20598 | − | 15.9452i | −0.298839 | − | 0.517604i | ||||
\(950\) | 3.77859 | − | 6.54470i | 0.122594 | − | 0.212338i | ||||
\(951\) | 14.4553 | − | 7.14590i | 0.468744 | − | 0.231722i | ||||
\(952\) | −4.73184 | + | 15.9888i | −0.153360 | + | 0.518200i | ||||
\(953\) | 7.20297i | 0.233327i | 0.993171 | + | 0.116664i | \(0.0372199\pi\) | ||||
−0.993171 | + | 0.116664i | \(0.962780\pi\) | |||||||
\(954\) | 3.75176 | + | 9.00831i | 0.121468 | + | 0.291655i | ||||
\(955\) | −4.30564 | + | 2.48586i | −0.139327 | + | 0.0804406i | ||||
\(956\) | −9.28556 | + | 5.36102i | −0.300317 | + | 0.173388i | ||||
\(957\) | 15.2922 | + | 0.987477i | 0.494327 | + | 0.0319206i | ||||
\(958\) | − | 23.0447i | − | 0.744540i | ||||||
\(959\) | −0.931789 | + | 3.14850i | −0.0300890 | + | 0.101670i | ||||
\(960\) | 0.767566 | + | 1.55269i | 0.0247731 | + | 0.0501128i | ||||
\(961\) | −5.90109 | + | 10.2210i | −0.190358 | + | 0.329709i | ||||
\(962\) | 17.2762 | + | 29.9232i | 0.557006 | + | 0.964762i | ||||
\(963\) | −3.24824 | + | 25.0465i | −0.104673 | + | 0.807111i | ||||
\(964\) | 1.02594 | + | 0.592325i | 0.0330432 | + | 0.0190775i | ||||
\(965\) | 6.03321 | 0.194216 | ||||||||
\(966\) | 22.4297 | − | 18.7005i | 0.721663 | − | 0.601680i | ||||
\(967\) | −12.2448 | −0.393765 | −0.196883 | − | 0.980427i | \(-0.563082\pi\) | ||||
−0.196883 | + | 0.980427i | \(0.563082\pi\) | |||||||
\(968\) | −4.91787 | − | 2.83934i | −0.158066 | − | 0.0912597i | ||||
\(969\) | 68.6349 | + | 45.7646i | 2.20487 | + | 1.47017i | ||||
\(970\) | 2.30861 | + | 3.99864i | 0.0741251 | + | 0.128388i | ||||
\(971\) | −13.4388 | + | 23.2768i | −0.431273 | + | 0.746987i | −0.996983 | − | 0.0776173i | \(-0.975269\pi\) |
0.565710 | + | 0.824604i | \(0.308602\pi\) | |||||||
\(972\) | 11.6703 | − | 10.3346i | 0.374324 | − | 0.331484i | ||||
\(973\) | 22.8337 | + | 24.0499i | 0.732014 | + | 0.771003i | ||||
\(974\) | 10.6277i | 0.340533i | ||||||||
\(975\) | −0.558158 | + | 8.64371i | −0.0178753 | + | 0.276820i | ||||
\(976\) | 5.18202 | − | 2.99184i | 0.165872 | − | 0.0957664i | ||||
\(977\) | −31.8298 | + | 18.3770i | −1.01833 | + | 0.587931i | −0.913619 | − | 0.406572i | \(-0.866724\pi\) |
−0.104707 | + | 0.994503i | \(0.533391\pi\) | |||||||
\(978\) | −0.961746 | + | 14.8937i | −0.0307533 | + | 0.476249i | ||||
\(979\) | 13.5819i | 0.434078i | ||||||||
\(980\) | −0.362928 | + | 6.99059i | −0.0115933 | + | 0.223306i | ||||
\(981\) | 12.1381 | − | 15.8821i | 0.387540 | − | 0.507076i | ||||
\(982\) | −11.2343 | + | 19.4584i | −0.358502 | + | 0.620943i | ||||
\(983\) | 6.68519 | + | 11.5791i | 0.213224 | + | 0.369315i | 0.952722 | − | 0.303844i | \(-0.0982702\pi\) |
−0.739498 | + | 0.673159i | \(0.764937\pi\) | |||||||
\(984\) | −14.1135 | − | 9.41063i | −0.449921 | − | 0.300000i | ||||
\(985\) | −12.3100 | − | 7.10719i | −0.392230 | − | 0.226454i | ||||
\(986\) | −24.1714 | −0.769775 | ||||||||
\(987\) | 7.12645 | + | 2.61929i | 0.226837 | + | 0.0833730i | ||||
\(988\) | −37.7922 | −1.20233 | ||||||||
\(989\) | 14.0883 | + | 8.13388i | 0.447982 | + | 0.258642i | ||||
\(990\) | 6.86293 | + | 0.890043i | 0.218118 | + | 0.0282874i | ||||
\(991\) | −8.34843 | − | 14.4599i | −0.265197 | − | 0.459334i | 0.702419 | − | 0.711764i | \(-0.252104\pi\) |
−0.967615 | + | 0.252430i | \(0.918770\pi\) | |||||||
\(992\) | 2.19077 | − | 3.79452i | 0.0695569 | − | 0.120476i | ||||
\(993\) | −14.0434 | − | 28.4080i | −0.445654 | − | 0.901501i | ||||
\(994\) | −1.76769 | − | 7.35502i | −0.0560677 | − | 0.233287i | ||||
\(995\) | 2.25088i | 0.0713576i | ||||||||
\(996\) | 3.17590 | + | 0.205080i | 0.100632 | + | 0.00649822i | ||||
\(997\) | 42.5957 | − | 24.5927i | 1.34902 | − | 0.778857i | 0.360910 | − | 0.932601i | \(-0.382466\pi\) |
0.988111 | + | 0.153743i | \(0.0491329\pi\) | |||||||
\(998\) | 34.4322 | − | 19.8794i | 1.08993 | − | 0.629272i | ||||
\(999\) | 23.5934 | − | 27.0608i | 0.746462 | − | 0.856167i |
(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.r.b.131.4 | yes | 12 | |
3.2 | odd | 2 | 210.2.r.a.131.1 | yes | 12 | ||
5.2 | odd | 4 | 1050.2.u.e.299.6 | 12 | |||
5.3 | odd | 4 | 1050.2.u.h.299.1 | 12 | |||
5.4 | even | 2 | 1050.2.s.f.551.3 | 12 | |||
7.2 | even | 3 | 1470.2.b.a.881.3 | 12 | |||
7.3 | odd | 6 | 210.2.r.a.101.1 | ✓ | 12 | ||
7.5 | odd | 6 | 1470.2.b.b.881.4 | 12 | |||
15.2 | even | 4 | 1050.2.u.g.299.4 | 12 | |||
15.8 | even | 4 | 1050.2.u.f.299.3 | 12 | |||
15.14 | odd | 2 | 1050.2.s.g.551.6 | 12 | |||
21.2 | odd | 6 | 1470.2.b.b.881.10 | 12 | |||
21.5 | even | 6 | 1470.2.b.a.881.9 | 12 | |||
21.17 | even | 6 | inner | 210.2.r.b.101.4 | yes | 12 | |
35.3 | even | 12 | 1050.2.u.g.899.4 | 12 | |||
35.17 | even | 12 | 1050.2.u.f.899.3 | 12 | |||
35.24 | odd | 6 | 1050.2.s.g.101.6 | 12 | |||
105.17 | odd | 12 | 1050.2.u.h.899.1 | 12 | |||
105.38 | odd | 12 | 1050.2.u.e.899.6 | 12 | |||
105.59 | even | 6 | 1050.2.s.f.101.3 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.2.r.a.101.1 | ✓ | 12 | 7.3 | odd | 6 | ||
210.2.r.a.131.1 | yes | 12 | 3.2 | odd | 2 | ||
210.2.r.b.101.4 | yes | 12 | 21.17 | even | 6 | inner | |
210.2.r.b.131.4 | yes | 12 | 1.1 | even | 1 | trivial | |
1050.2.s.f.101.3 | 12 | 105.59 | even | 6 | |||
1050.2.s.f.551.3 | 12 | 5.4 | even | 2 | |||
1050.2.s.g.101.6 | 12 | 35.24 | odd | 6 | |||
1050.2.s.g.551.6 | 12 | 15.14 | odd | 2 | |||
1050.2.u.e.299.6 | 12 | 5.2 | odd | 4 | |||
1050.2.u.e.899.6 | 12 | 105.38 | odd | 12 | |||
1050.2.u.f.299.3 | 12 | 15.8 | even | 4 | |||
1050.2.u.f.899.3 | 12 | 35.17 | even | 12 | |||
1050.2.u.g.299.4 | 12 | 15.2 | even | 4 | |||
1050.2.u.g.899.4 | 12 | 35.3 | even | 12 | |||
1050.2.u.h.299.1 | 12 | 5.3 | odd | 4 | |||
1050.2.u.h.899.1 | 12 | 105.17 | odd | 12 | |||
1470.2.b.a.881.3 | 12 | 7.2 | even | 3 | |||
1470.2.b.a.881.9 | 12 | 21.5 | even | 6 | |||
1470.2.b.b.881.4 | 12 | 7.5 | odd | 6 | |||
1470.2.b.b.881.10 | 12 | 21.2 | odd | 6 |