Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1110,2,Mod(961,1110)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1110, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("1110.961");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1110.h (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.86339462436\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.279290944.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 26x^{4} + 169x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{37}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 961.4 | ||
Root | \(3.44055i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1110.961 |
Dual form | 1110.2.h.f.961.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).
\(n\) | \(371\) | \(631\) | \(667\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 1.00000i | 0.447214i | ||||||||
\(6\) | 1.00000i | 0.408248i | ||||||||
\(7\) | −4.44055 | −1.67837 | −0.839185 | − | 0.543845i | \(-0.816968\pi\) | ||||
−0.839185 | + | 0.543845i | \(0.816968\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | −2.44055 | −0.735854 | −0.367927 | − | 0.929855i | \(-0.619932\pi\) | ||||
−0.367927 | + | 0.929855i | \(0.619932\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 0.440552i | 0.122187i | 0.998132 | + | 0.0610935i | \(0.0194588\pi\) | ||||
−0.998132 | + | 0.0610935i | \(0.980541\pi\) | |||||||
\(14\) | − | 4.44055i | − | 1.18679i | ||||||
\(15\) | 1.00000i | 0.258199i | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − | 4.83740i | − | 1.17324i | −0.809862 | − | 0.586620i | \(-0.800458\pi\) | ||
0.809862 | − | 0.586620i | \(-0.199542\pi\) | |||||||
\(18\) | 1.00000i | 0.235702i | ||||||||
\(19\) | − | 0.440552i | − | 0.101069i | −0.998722 | − | 0.0505347i | \(-0.983907\pi\) | ||
0.998722 | − | 0.0505347i | \(-0.0160926\pi\) | |||||||
\(20\) | − | 1.00000i | − | 0.223607i | ||||||
\(21\) | −4.44055 | −0.969008 | ||||||||
\(22\) | − | 2.44055i | − | 0.520327i | ||||||
\(23\) | − | 2.83740i | − | 0.591638i | −0.955244 | − | 0.295819i | \(-0.904407\pi\) | ||
0.955244 | − | 0.295819i | \(-0.0955925\pi\) | |||||||
\(24\) | − | 1.00000i | − | 0.204124i | ||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | −0.440552 | −0.0863993 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 4.44055 | 0.839185 | ||||||||
\(29\) | − | 2.00000i | − | 0.371391i | −0.982607 | − | 0.185695i | \(-0.940546\pi\) | ||
0.982607 | − | 0.185695i | \(-0.0594537\pi\) | |||||||
\(30\) | −1.00000 | −0.182574 | ||||||||
\(31\) | − | 5.27795i | − | 0.947947i | −0.880539 | − | 0.473974i | \(-0.842819\pi\) | ||
0.880539 | − | 0.473974i | \(-0.157181\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | −2.44055 | −0.424846 | ||||||||
\(34\) | 4.83740 | 0.829607 | ||||||||
\(35\) | − | 4.44055i | − | 0.750590i | ||||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | −0.198422 | − | 6.07953i | −0.0326204 | − | 0.999468i | ||||
\(38\) | 0.440552 | 0.0714669 | ||||||||
\(39\) | 0.440552i | 0.0705447i | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | −2.00000 | −0.312348 | −0.156174 | − | 0.987730i | \(-0.549916\pi\) | ||||
−0.156174 | + | 0.987730i | \(0.549916\pi\) | |||||||
\(42\) | − | 4.44055i | − | 0.685192i | ||||||
\(43\) | 0.396844i | 0.0605182i | 0.999542 | + | 0.0302591i | \(0.00963323\pi\) | ||||
−0.999542 | + | 0.0302591i | \(0.990367\pi\) | |||||||
\(44\) | 2.44055 | 0.367927 | ||||||||
\(45\) | 1.00000i | 0.149071i | ||||||||
\(46\) | 2.83740 | 0.418351 | ||||||||
\(47\) | −10.8811 | −1.58717 | −0.793586 | − | 0.608458i | \(-0.791788\pi\) | ||||
−0.793586 | + | 0.608458i | \(0.791788\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 12.7185 | 1.81693 | ||||||||
\(50\) | − | 1.00000i | − | 0.141421i | ||||||
\(51\) | − | 4.83740i | − | 0.677371i | ||||||
\(52\) | − | 0.440552i | − | 0.0610935i | ||||||
\(53\) | −2.44055 | −0.335236 | −0.167618 | − | 0.985852i | \(-0.553607\pi\) | ||||
−0.167618 | + | 0.985852i | \(0.553607\pi\) | |||||||
\(54\) | 1.00000i | 0.136083i | ||||||||
\(55\) | − | 2.44055i | − | 0.329084i | ||||||
\(56\) | 4.44055i | 0.593394i | ||||||||
\(57\) | − | 0.440552i | − | 0.0583525i | ||||||
\(58\) | 2.00000 | 0.262613 | ||||||||
\(59\) | 2.39684i | 0.312043i | 0.987754 | + | 0.156021i | \(0.0498668\pi\) | ||||
−0.987754 | + | 0.156021i | \(0.950133\pi\) | |||||||
\(60\) | − | 1.00000i | − | 0.129099i | ||||||
\(61\) | − | 2.00000i | − | 0.256074i | −0.991769 | − | 0.128037i | \(-0.959132\pi\) | ||
0.991769 | − | 0.128037i | \(-0.0408676\pi\) | |||||||
\(62\) | 5.27795 | 0.670300 | ||||||||
\(63\) | −4.44055 | −0.559457 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −0.440552 | −0.0546437 | ||||||||
\(66\) | − | 2.44055i | − | 0.300411i | ||||||
\(67\) | −13.7622 | −1.68132 | −0.840661 | − | 0.541562i | \(-0.817833\pi\) | ||||
−0.840661 | + | 0.541562i | \(0.817833\pi\) | |||||||
\(68\) | 4.83740i | 0.586620i | ||||||||
\(69\) | − | 2.83740i | − | 0.341582i | ||||||
\(70\) | 4.44055 | 0.530747 | ||||||||
\(71\) | −9.67479 | −1.14819 | −0.574093 | − | 0.818790i | \(-0.694645\pi\) | ||||
−0.574093 | + | 0.818790i | \(0.694645\pi\) | |||||||
\(72\) | − | 1.00000i | − | 0.117851i | ||||||
\(73\) | 5.71850 | 0.669300 | 0.334650 | − | 0.942343i | \(-0.391382\pi\) | ||||
0.334650 | + | 0.942343i | \(0.391382\pi\) | |||||||
\(74\) | 6.07953 | − | 0.198422i | 0.706730 | − | 0.0230661i | ||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 0.440552i | 0.0505347i | ||||||||
\(77\) | 10.8374 | 1.23504 | ||||||||
\(78\) | −0.440552 | −0.0498827 | ||||||||
\(79\) | 13.2779i | 1.49389i | 0.664888 | + | 0.746943i | \(0.268479\pi\) | ||||
−0.664888 | + | 0.746943i | \(0.731521\pi\) | |||||||
\(80\) | 1.00000i | 0.111803i | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | − | 2.00000i | − | 0.220863i | ||||||
\(83\) | −7.71850 | −0.847215 | −0.423608 | − | 0.905846i | \(-0.639236\pi\) | ||||
−0.423608 | + | 0.905846i | \(0.639236\pi\) | |||||||
\(84\) | 4.44055 | 0.484504 | ||||||||
\(85\) | 4.83740 | 0.524689 | ||||||||
\(86\) | −0.396844 | −0.0427928 | ||||||||
\(87\) | − | 2.00000i | − | 0.214423i | ||||||
\(88\) | 2.44055i | 0.260164i | ||||||||
\(89\) | 15.3217i | 1.62409i | 0.583593 | + | 0.812046i | \(0.301646\pi\) | ||||
−0.583593 | + | 0.812046i | \(0.698354\pi\) | |||||||
\(90\) | −1.00000 | −0.105409 | ||||||||
\(91\) | − | 1.95629i | − | 0.205075i | ||||||
\(92\) | 2.83740i | 0.295819i | ||||||||
\(93\) | − | 5.27795i | − | 0.547298i | ||||||
\(94\) | − | 10.8811i | − | 1.12230i | ||||||
\(95\) | 0.440552 | 0.0451996 | ||||||||
\(96\) | 1.00000i | 0.102062i | ||||||||
\(97\) | − | 2.88110i | − | 0.292532i | −0.989245 | − | 0.146266i | \(-0.953275\pi\) | ||
0.989245 | − | 0.146266i | \(-0.0467255\pi\) | |||||||
\(98\) | 12.7185i | 1.28476i | ||||||||
\(99\) | −2.44055 | −0.245285 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −12.1591 | −1.20987 | −0.604935 | − | 0.796275i | \(-0.706801\pi\) | ||||
−0.604935 | + | 0.796275i | \(0.706801\pi\) | |||||||
\(102\) | 4.83740 | 0.478974 | ||||||||
\(103\) | − | 10.5559i | − | 1.04010i | −0.854135 | − | 0.520052i | \(-0.825913\pi\) | ||
0.854135 | − | 0.520052i | \(-0.174087\pi\) | |||||||
\(104\) | 0.440552 | 0.0431996 | ||||||||
\(105\) | − | 4.44055i | − | 0.433353i | ||||||
\(106\) | − | 2.44055i | − | 0.237047i | ||||||
\(107\) | 18.9248 | 1.82953 | 0.914765 | − | 0.403986i | \(-0.132375\pi\) | ||||
0.914765 | + | 0.403986i | \(0.132375\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | − | 12.0437i | − | 1.15358i | −0.816893 | − | 0.576789i | \(-0.804305\pi\) | ||
0.816893 | − | 0.576789i | \(-0.195695\pi\) | |||||||
\(110\) | 2.44055 | 0.232697 | ||||||||
\(111\) | −0.198422 | − | 6.07953i | −0.0188334 | − | 0.577043i | ||||
\(112\) | −4.44055 | −0.419593 | ||||||||
\(113\) | 2.00000i | 0.188144i | 0.995565 | + | 0.0940721i | \(0.0299884\pi\) | ||||
−0.995565 | + | 0.0940721i | \(0.970012\pi\) | |||||||
\(114\) | 0.440552 | 0.0412614 | ||||||||
\(115\) | 2.83740 | 0.264589 | ||||||||
\(116\) | 2.00000i | 0.185695i | ||||||||
\(117\) | 0.440552i | 0.0407290i | ||||||||
\(118\) | −2.39684 | −0.220647 | ||||||||
\(119\) | 21.4807i | 1.96913i | ||||||||
\(120\) | 1.00000 | 0.0912871 | ||||||||
\(121\) | −5.04371 | −0.458519 | ||||||||
\(122\) | 2.00000 | 0.181071 | ||||||||
\(123\) | −2.00000 | −0.180334 | ||||||||
\(124\) | 5.27795i | 0.473974i | ||||||||
\(125\) | − | 1.00000i | − | 0.0894427i | ||||||
\(126\) | − | 4.44055i | − | 0.395596i | ||||||
\(127\) | −7.55945 | −0.670793 | −0.335396 | − | 0.942077i | \(-0.608870\pi\) | ||||
−0.335396 | + | 0.942077i | \(0.608870\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | 0.396844i | 0.0349402i | ||||||||
\(130\) | − | 0.440552i | − | 0.0386389i | ||||||
\(131\) | 12.1591i | 1.06234i | 0.847265 | + | 0.531171i | \(0.178248\pi\) | ||||
−0.847265 | + | 0.531171i | \(0.821752\pi\) | |||||||
\(132\) | 2.44055 | 0.212423 | ||||||||
\(133\) | 1.95629i | 0.169632i | ||||||||
\(134\) | − | 13.7622i | − | 1.18887i | ||||||
\(135\) | 1.00000i | 0.0860663i | ||||||||
\(136\) | −4.83740 | −0.414803 | ||||||||
\(137\) | 3.27795 | 0.280054 | 0.140027 | − | 0.990148i | \(-0.455281\pi\) | ||||
0.140027 | + | 0.990148i | \(0.455281\pi\) | |||||||
\(138\) | 2.83740 | 0.241535 | ||||||||
\(139\) | 5.76221 | 0.488744 | 0.244372 | − | 0.969682i | \(-0.421418\pi\) | ||||
0.244372 | + | 0.969682i | \(0.421418\pi\) | |||||||
\(140\) | 4.44055i | 0.375295i | ||||||||
\(141\) | −10.8811 | −0.916354 | ||||||||
\(142\) | − | 9.67479i | − | 0.811890i | ||||||
\(143\) | − | 1.07519i | − | 0.0899118i | ||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 2.00000 | 0.166091 | ||||||||
\(146\) | 5.71850i | 0.473266i | ||||||||
\(147\) | 12.7185 | 1.04900 | ||||||||
\(148\) | 0.198422 | + | 6.07953i | 0.0163102 | + | 0.499734i | ||||
\(149\) | 1.60316 | 0.131336 | 0.0656678 | − | 0.997842i | \(-0.479082\pi\) | ||||
0.0656678 | + | 0.997842i | \(0.479082\pi\) | |||||||
\(150\) | − | 1.00000i | − | 0.0816497i | ||||||
\(151\) | 4.28150 | 0.348424 | 0.174212 | − | 0.984708i | \(-0.444262\pi\) | ||||
0.174212 | + | 0.984708i | \(0.444262\pi\) | |||||||
\(152\) | −0.440552 | −0.0357335 | ||||||||
\(153\) | − | 4.83740i | − | 0.391080i | ||||||
\(154\) | 10.8374i | 0.873302i | ||||||||
\(155\) | 5.27795 | 0.423935 | ||||||||
\(156\) | − | 0.440552i | − | 0.0352724i | ||||||
\(157\) | 3.60316 | 0.287563 | 0.143782 | − | 0.989609i | \(-0.454074\pi\) | ||||
0.143782 | + | 0.989609i | \(0.454074\pi\) | |||||||
\(158\) | −13.2779 | −1.05634 | ||||||||
\(159\) | −2.44055 | −0.193548 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | 12.5996i | 0.992988i | ||||||||
\(162\) | 1.00000i | 0.0785674i | ||||||||
\(163\) | − | 3.32165i | − | 0.260172i | −0.991503 | − | 0.130086i | \(-0.958475\pi\) | ||
0.991503 | − | 0.130086i | \(-0.0415254\pi\) | |||||||
\(164\) | 2.00000 | 0.156174 | ||||||||
\(165\) | − | 2.44055i | − | 0.189997i | ||||||
\(166\) | − | 7.71850i | − | 0.599072i | ||||||
\(167\) | 2.83740i | 0.219564i | 0.993956 | + | 0.109782i | \(0.0350153\pi\) | ||||
−0.993956 | + | 0.109782i | \(0.964985\pi\) | |||||||
\(168\) | 4.44055i | 0.342596i | ||||||||
\(169\) | 12.8059 | 0.985070 | ||||||||
\(170\) | 4.83740i | 0.371011i | ||||||||
\(171\) | − | 0.440552i | − | 0.0336898i | ||||||
\(172\) | − | 0.396844i | − | 0.0302591i | ||||||
\(173\) | −12.9964 | −0.988102 | −0.494051 | − | 0.869433i | \(-0.664484\pi\) | ||||
−0.494051 | + | 0.869433i | \(0.664484\pi\) | |||||||
\(174\) | 2.00000 | 0.151620 | ||||||||
\(175\) | 4.44055 | 0.335674 | ||||||||
\(176\) | −2.44055 | −0.183964 | ||||||||
\(177\) | 2.39684i | 0.180158i | ||||||||
\(178\) | −15.3217 | −1.14841 | ||||||||
\(179\) | − | 4.72205i | − | 0.352943i | −0.984306 | − | 0.176471i | \(-0.943532\pi\) | ||
0.984306 | − | 0.176471i | \(-0.0564683\pi\) | |||||||
\(180\) | − | 1.00000i | − | 0.0745356i | ||||||
\(181\) | 20.5559 | 1.52791 | 0.763954 | − | 0.645271i | \(-0.223256\pi\) | ||||
0.763954 | + | 0.645271i | \(0.223256\pi\) | |||||||
\(182\) | 1.95629 | 0.145010 | ||||||||
\(183\) | − | 2.00000i | − | 0.147844i | ||||||
\(184\) | −2.83740 | −0.209176 | ||||||||
\(185\) | 6.07953 | − | 0.198422i | 0.446976 | − | 0.0145883i | ||||
\(186\) | 5.27795 | 0.386998 | ||||||||
\(187\) | 11.8059i | 0.863334i | ||||||||
\(188\) | 10.8811 | 0.793586 | ||||||||
\(189\) | −4.44055 | −0.323003 | ||||||||
\(190\) | 0.440552i | 0.0319610i | ||||||||
\(191\) | 9.16260i | 0.662983i | 0.943458 | + | 0.331491i | \(0.107552\pi\) | ||||
−0.943458 | + | 0.331491i | \(0.892448\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | − | 14.8811i | − | 1.07117i | −0.844483 | − | 0.535583i | \(-0.820092\pi\) | ||
0.844483 | − | 0.535583i | \(-0.179908\pi\) | |||||||
\(194\) | 2.88110 | 0.206851 | ||||||||
\(195\) | −0.440552 | −0.0315486 | ||||||||
\(196\) | −12.7185 | −0.908464 | ||||||||
\(197\) | −9.55945 | −0.681082 | −0.340541 | − | 0.940230i | \(-0.610610\pi\) | ||||
−0.340541 | + | 0.940230i | \(0.610610\pi\) | |||||||
\(198\) | − | 2.44055i | − | 0.173442i | ||||||
\(199\) | − | 20.4843i | − | 1.45209i | −0.687647 | − | 0.726045i | \(-0.741356\pi\) | ||
0.687647 | − | 0.726045i | \(-0.258644\pi\) | |||||||
\(200\) | 1.00000i | 0.0707107i | ||||||||
\(201\) | −13.7622 | −0.970711 | ||||||||
\(202\) | − | 12.1591i | − | 0.855508i | ||||||
\(203\) | 8.88110i | 0.623331i | ||||||||
\(204\) | 4.83740i | 0.338685i | ||||||||
\(205\) | − | 2.00000i | − | 0.139686i | ||||||
\(206\) | 10.5559 | 0.735464 | ||||||||
\(207\) | − | 2.83740i | − | 0.197213i | ||||||
\(208\) | 0.440552i | 0.0305468i | ||||||||
\(209\) | 1.07519i | 0.0743724i | ||||||||
\(210\) | 4.44055 | 0.306427 | ||||||||
\(211\) | 0.881103 | 0.0606577 | 0.0303288 | − | 0.999540i | \(-0.490345\pi\) | ||||
0.0303288 | + | 0.999540i | \(0.490345\pi\) | |||||||
\(212\) | 2.44055 | 0.167618 | ||||||||
\(213\) | −9.67479 | −0.662906 | ||||||||
\(214\) | 18.9248i | 1.29367i | ||||||||
\(215\) | −0.396844 | −0.0270645 | ||||||||
\(216\) | − | 1.00000i | − | 0.0680414i | ||||||
\(217\) | 23.4370i | 1.59101i | ||||||||
\(218\) | 12.0437 | 0.815703 | ||||||||
\(219\) | 5.71850 | 0.386420 | ||||||||
\(220\) | 2.44055i | 0.164542i | ||||||||
\(221\) | 2.13112 | 0.143355 | ||||||||
\(222\) | 6.07953 | − | 0.198422i | 0.408031 | − | 0.0133172i | ||||
\(223\) | 1.51574 | 0.101502 | 0.0507508 | − | 0.998711i | \(-0.483839\pi\) | ||||
0.0507508 | + | 0.998711i | \(0.483839\pi\) | |||||||
\(224\) | − | 4.44055i | − | 0.296697i | ||||||
\(225\) | −1.00000 | −0.0666667 | ||||||||
\(226\) | −2.00000 | −0.133038 | ||||||||
\(227\) | − | 14.5559i | − | 0.966109i | −0.875590 | − | 0.483054i | \(-0.839527\pi\) | ||
0.875590 | − | 0.483054i | \(-0.160473\pi\) | |||||||
\(228\) | 0.440552i | 0.0291762i | ||||||||
\(229\) | 15.6748 | 1.03582 | 0.517910 | − | 0.855435i | \(-0.326710\pi\) | ||||
0.517910 | + | 0.855435i | \(0.326710\pi\) | |||||||
\(230\) | 2.83740i | 0.187092i | ||||||||
\(231\) | 10.8374 | 0.713048 | ||||||||
\(232\) | −2.00000 | −0.131306 | ||||||||
\(233\) | −11.2779 | −0.738843 | −0.369421 | − | 0.929262i | \(-0.620444\pi\) | ||||
−0.369421 | + | 0.929262i | \(0.620444\pi\) | |||||||
\(234\) | −0.440552 | −0.0287998 | ||||||||
\(235\) | − | 10.8811i | − | 0.709805i | ||||||
\(236\) | − | 2.39684i | − | 0.156021i | ||||||
\(237\) | 13.2779i | 0.862495i | ||||||||
\(238\) | −21.4807 | −1.39239 | ||||||||
\(239\) | 22.5559i | 1.45902i | 0.683970 | + | 0.729510i | \(0.260252\pi\) | ||||
−0.683970 | + | 0.729510i | \(0.739748\pi\) | |||||||
\(240\) | 1.00000i | 0.0645497i | ||||||||
\(241\) | 26.5559i | 1.71062i | 0.518120 | + | 0.855308i | \(0.326632\pi\) | ||||
−0.518120 | + | 0.855308i | \(0.673368\pi\) | |||||||
\(242\) | − | 5.04371i | − | 0.324222i | ||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 2.00000i | 0.128037i | ||||||||
\(245\) | 12.7185i | 0.812555i | ||||||||
\(246\) | − | 2.00000i | − | 0.127515i | ||||||
\(247\) | 0.194086 | 0.0123494 | ||||||||
\(248\) | −5.27795 | −0.335150 | ||||||||
\(249\) | −7.71850 | −0.489140 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | 3.27795i | 0.206902i | 0.994635 | + | 0.103451i | \(0.0329885\pi\) | ||||
−0.994635 | + | 0.103451i | \(0.967011\pi\) | |||||||
\(252\) | 4.44055 | 0.279728 | ||||||||
\(253\) | 6.92481i | 0.435359i | ||||||||
\(254\) | − | 7.55945i | − | 0.474322i | ||||||
\(255\) | 4.83740 | 0.302929 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − | 20.0437i | − | 1.25029i | −0.780508 | − | 0.625146i | \(-0.785039\pi\) | ||
0.780508 | − | 0.625146i | \(-0.214961\pi\) | |||||||
\(258\) | −0.396844 | −0.0247064 | ||||||||
\(259\) | 0.881103 | + | 26.9964i | 0.0547491 | + | 1.67748i | ||||
\(260\) | 0.440552 | 0.0273219 | ||||||||
\(261\) | − | 2.00000i | − | 0.123797i | ||||||
\(262\) | −12.1591 | −0.751189 | ||||||||
\(263\) | −17.4370 | −1.07521 | −0.537606 | − | 0.843196i | \(-0.680671\pi\) | ||||
−0.537606 | + | 0.843196i | \(0.680671\pi\) | |||||||
\(264\) | 2.44055i | 0.150206i | ||||||||
\(265\) | − | 2.44055i | − | 0.149922i | ||||||
\(266\) | −1.95629 | −0.119948 | ||||||||
\(267\) | 15.3217i | 0.937670i | ||||||||
\(268\) | 13.7622 | 0.840661 | ||||||||
\(269\) | −16.4406 | −1.00240 | −0.501199 | − | 0.865332i | \(-0.667108\pi\) | ||||
−0.501199 | + | 0.865332i | \(0.667108\pi\) | |||||||
\(270\) | −1.00000 | −0.0608581 | ||||||||
\(271\) | −24.3181 | −1.47722 | −0.738610 | − | 0.674133i | \(-0.764517\pi\) | ||||
−0.738610 | + | 0.674133i | \(0.764517\pi\) | |||||||
\(272\) | − | 4.83740i | − | 0.293310i | ||||||
\(273\) | − | 1.95629i | − | 0.118400i | ||||||
\(274\) | 3.27795i | 0.198028i | ||||||||
\(275\) | 2.44055 | 0.147171 | ||||||||
\(276\) | 2.83740i | 0.170791i | ||||||||
\(277\) | − | 0.353137i | − | 0.0212179i | −0.999944 | − | 0.0106090i | \(-0.996623\pi\) | ||
0.999944 | − | 0.0106090i | \(-0.00337700\pi\) | |||||||
\(278\) | 5.76221i | 0.345594i | ||||||||
\(279\) | − | 5.27795i | − | 0.315982i | ||||||
\(280\) | −4.44055 | −0.265374 | ||||||||
\(281\) | 20.2028i | 1.20520i | 0.798045 | + | 0.602598i | \(0.205868\pi\) | ||||
−0.798045 | + | 0.602598i | \(0.794132\pi\) | |||||||
\(282\) | − | 10.8811i | − | 0.647960i | ||||||
\(283\) | 13.6469i | 0.811222i | 0.914046 | + | 0.405611i | \(0.132941\pi\) | ||||
−0.914046 | + | 0.405611i | \(0.867059\pi\) | |||||||
\(284\) | 9.67479 | 0.574093 | ||||||||
\(285\) | 0.440552 | 0.0260960 | ||||||||
\(286\) | 1.07519 | 0.0635773 | ||||||||
\(287\) | 8.88110 | 0.524235 | ||||||||
\(288\) | 1.00000i | 0.0589256i | ||||||||
\(289\) | −6.40040 | −0.376494 | ||||||||
\(290\) | 2.00000i | 0.117444i | ||||||||
\(291\) | − | 2.88110i | − | 0.168893i | ||||||
\(292\) | −5.71850 | −0.334650 | ||||||||
\(293\) | −6.44055 | −0.376261 | −0.188131 | − | 0.982144i | \(-0.560243\pi\) | ||||
−0.188131 | + | 0.982144i | \(0.560243\pi\) | |||||||
\(294\) | 12.7185i | 0.741758i | ||||||||
\(295\) | −2.39684 | −0.139550 | ||||||||
\(296\) | −6.07953 | + | 0.198422i | −0.353365 | + | 0.0115330i | ||||
\(297\) | −2.44055 | −0.141615 | ||||||||
\(298\) | 1.60316i | 0.0928683i | ||||||||
\(299\) | 1.25002 | 0.0722905 | ||||||||
\(300\) | 1.00000 | 0.0577350 | ||||||||
\(301\) | − | 1.76221i | − | 0.101572i | ||||||
\(302\) | 4.28150i | 0.246373i | ||||||||
\(303\) | −12.1591 | −0.698519 | ||||||||
\(304\) | − | 0.440552i | − | 0.0252674i | ||||||
\(305\) | 2.00000 | 0.114520 | ||||||||
\(306\) | 4.83740 | 0.276536 | ||||||||
\(307\) | −20.3181 | −1.15962 | −0.579808 | − | 0.814753i | \(-0.696872\pi\) | ||||
−0.579808 | + | 0.814753i | \(0.696872\pi\) | |||||||
\(308\) | −10.8374 | −0.617518 | ||||||||
\(309\) | − | 10.5559i | − | 0.600504i | ||||||
\(310\) | 5.27795i | 0.299767i | ||||||||
\(311\) | − | 6.23779i | − | 0.353713i | −0.984237 | − | 0.176856i | \(-0.943407\pi\) | ||
0.984237 | − | 0.176856i | \(-0.0565928\pi\) | |||||||
\(312\) | 0.440552 | 0.0249413 | ||||||||
\(313\) | 8.55589i | 0.483608i | 0.970325 | + | 0.241804i | \(0.0777391\pi\) | ||||
−0.970325 | + | 0.241804i | \(0.922261\pi\) | |||||||
\(314\) | 3.60316i | 0.203338i | ||||||||
\(315\) | − | 4.44055i | − | 0.250197i | ||||||
\(316\) | − | 13.2779i | − | 0.746943i | ||||||
\(317\) | −33.5960 | −1.88694 | −0.943471 | − | 0.331455i | \(-0.892461\pi\) | ||||
−0.943471 | + | 0.331455i | \(0.892461\pi\) | |||||||
\(318\) | − | 2.44055i | − | 0.136859i | ||||||
\(319\) | 4.88110i | 0.273289i | ||||||||
\(320\) | − | 1.00000i | − | 0.0559017i | ||||||
\(321\) | 18.9248 | 1.05628 | ||||||||
\(322\) | −12.5996 | −0.702148 | ||||||||
\(323\) | −2.13112 | −0.118579 | ||||||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | − | 0.440552i | − | 0.0244374i | ||||||
\(326\) | 3.32165 | 0.183969 | ||||||||
\(327\) | − | 12.0437i | − | 0.666019i | ||||||
\(328\) | 2.00000i | 0.110432i | ||||||||
\(329\) | 48.3181 | 2.66386 | ||||||||
\(330\) | 2.44055 | 0.134348 | ||||||||
\(331\) | − | 31.2779i | − | 1.71919i | −0.510975 | − | 0.859596i | \(-0.670715\pi\) | ||
0.510975 | − | 0.859596i | \(-0.329285\pi\) | |||||||
\(332\) | 7.71850 | 0.423608 | ||||||||
\(333\) | −0.198422 | − | 6.07953i | −0.0108735 | − | 0.333156i | ||||
\(334\) | −2.83740 | −0.155255 | ||||||||
\(335\) | − | 13.7622i | − | 0.751910i | ||||||
\(336\) | −4.44055 | −0.242252 | ||||||||
\(337\) | −5.63108 | −0.306745 | −0.153372 | − | 0.988168i | \(-0.549013\pi\) | ||||
−0.153372 | + | 0.988168i | \(0.549013\pi\) | |||||||
\(338\) | 12.8059i | 0.696550i | ||||||||
\(339\) | 2.00000i | 0.108625i | ||||||||
\(340\) | −4.83740 | −0.262345 | ||||||||
\(341\) | 12.8811i | 0.697551i | ||||||||
\(342\) | 0.440552 | 0.0238223 | ||||||||
\(343\) | −25.3933 | −1.37111 | ||||||||
\(344\) | 0.396844 | 0.0213964 | ||||||||
\(345\) | 2.83740 | 0.152760 | ||||||||
\(346\) | − | 12.9964i | − | 0.698693i | ||||||
\(347\) | − | 0.881103i | − | 0.0473001i | −0.999720 | − | 0.0236501i | \(-0.992471\pi\) | ||
0.999720 | − | 0.0236501i | \(-0.00752875\pi\) | |||||||
\(348\) | 2.00000i | 0.107211i | ||||||||
\(349\) | 0.555895 | 0.0297564 | 0.0148782 | − | 0.999889i | \(-0.495264\pi\) | ||||
0.0148782 | + | 0.999889i | \(0.495264\pi\) | |||||||
\(350\) | 4.44055i | 0.237357i | ||||||||
\(351\) | 0.440552i | 0.0235149i | ||||||||
\(352\) | − | 2.44055i | − | 0.130082i | ||||||
\(353\) | 5.20631i | 0.277104i | 0.990355 | + | 0.138552i | \(0.0442448\pi\) | ||||
−0.990355 | + | 0.138552i | \(0.955755\pi\) | |||||||
\(354\) | −2.39684 | −0.127391 | ||||||||
\(355\) | − | 9.67479i | − | 0.513485i | ||||||
\(356\) | − | 15.3217i | − | 0.812046i | ||||||
\(357\) | 21.4807i | 1.13688i | ||||||||
\(358\) | 4.72205 | 0.249568 | ||||||||
\(359\) | −15.4370 | −0.814734 | −0.407367 | − | 0.913265i | \(-0.633553\pi\) | ||||
−0.407367 | + | 0.913265i | \(0.633553\pi\) | |||||||
\(360\) | 1.00000 | 0.0527046 | ||||||||
\(361\) | 18.8059 | 0.989785 | ||||||||
\(362\) | 20.5559i | 1.08039i | ||||||||
\(363\) | −5.04371 | −0.264726 | ||||||||
\(364\) | 1.95629i | 0.102538i | ||||||||
\(365\) | 5.71850i | 0.299320i | ||||||||
\(366\) | 2.00000 | 0.104542 | ||||||||
\(367\) | −14.9964 | −0.782808 | −0.391404 | − | 0.920219i | \(-0.628011\pi\) | ||||
−0.391404 | + | 0.920219i | \(0.628011\pi\) | |||||||
\(368\) | − | 2.83740i | − | 0.147909i | ||||||
\(369\) | −2.00000 | −0.104116 | ||||||||
\(370\) | 0.198422 | + | 6.07953i | 0.0103155 | + | 0.316059i | ||||
\(371\) | 10.8374 | 0.562650 | ||||||||
\(372\) | 5.27795i | 0.273649i | ||||||||
\(373\) | 33.5086 | 1.73501 | 0.867506 | − | 0.497427i | \(-0.165722\pi\) | ||||
0.867506 | + | 0.497427i | \(0.165722\pi\) | |||||||
\(374\) | −11.8059 | −0.610469 | ||||||||
\(375\) | − | 1.00000i | − | 0.0516398i | ||||||
\(376\) | 10.8811i | 0.561150i | ||||||||
\(377\) | 0.881103 | 0.0453791 | ||||||||
\(378\) | − | 4.44055i | − | 0.228397i | ||||||
\(379\) | 34.6433 | 1.77951 | 0.889754 | − | 0.456441i | \(-0.150876\pi\) | ||||
0.889754 | + | 0.456441i | \(0.150876\pi\) | |||||||
\(380\) | −0.440552 | −0.0225998 | ||||||||
\(381\) | −7.55945 | −0.387282 | ||||||||
\(382\) | −9.16260 | −0.468800 | ||||||||
\(383\) | − | 8.51219i | − | 0.434952i | −0.976066 | − | 0.217476i | \(-0.930218\pi\) | ||
0.976066 | − | 0.217476i | \(-0.0697825\pi\) | |||||||
\(384\) | − | 1.00000i | − | 0.0510310i | ||||||
\(385\) | 10.8374i | 0.552325i | ||||||||
\(386\) | 14.8811 | 0.757428 | ||||||||
\(387\) | 0.396844i | 0.0201727i | ||||||||
\(388\) | 2.88110i | 0.146266i | ||||||||
\(389\) | − | 27.6748i | − | 1.40317i | −0.712587 | − | 0.701584i | \(-0.752477\pi\) | ||
0.712587 | − | 0.701584i | \(-0.247523\pi\) | |||||||
\(390\) | − | 0.440552i | − | 0.0223082i | ||||||
\(391\) | −13.7256 | −0.694134 | ||||||||
\(392\) | − | 12.7185i | − | 0.642381i | ||||||
\(393\) | 12.1591i | 0.613343i | ||||||||
\(394\) | − | 9.55945i | − | 0.481598i | ||||||
\(395\) | −13.2779 | −0.668086 | ||||||||
\(396\) | 2.44055 | 0.122642 | ||||||||
\(397\) | 9.36536 | 0.470034 | 0.235017 | − | 0.971991i | \(-0.424485\pi\) | ||||
0.235017 | + | 0.971991i | \(0.424485\pi\) | |||||||
\(398\) | 20.4843 | 1.02678 | ||||||||
\(399\) | 1.95629i | 0.0979371i | ||||||||
\(400\) | −1.00000 | −0.0500000 | ||||||||
\(401\) | − | 7.88466i | − | 0.393741i | −0.980430 | − | 0.196870i | \(-0.936922\pi\) | ||
0.980430 | − | 0.196870i | \(-0.0630778\pi\) | |||||||
\(402\) | − | 13.7622i | − | 0.686396i | ||||||
\(403\) | 2.32521 | 0.115827 | ||||||||
\(404\) | 12.1591 | 0.604935 | ||||||||
\(405\) | 1.00000i | 0.0496904i | ||||||||
\(406\) | −8.88110 | −0.440762 | ||||||||
\(407\) | 0.484259 | + | 14.8374i | 0.0240038 | + | 0.735462i | ||||
\(408\) | −4.83740 | −0.239487 | ||||||||
\(409\) | − | 38.7307i | − | 1.91511i | −0.288249 | − | 0.957556i | \(-0.593073\pi\) | ||
0.288249 | − | 0.957556i | \(-0.406927\pi\) | |||||||
\(410\) | 2.00000 | 0.0987730 | ||||||||
\(411\) | 3.27795 | 0.161689 | ||||||||
\(412\) | 10.5559i | 0.520052i | ||||||||
\(413\) | − | 10.6433i | − | 0.523723i | ||||||
\(414\) | 2.83740 | 0.139450 | ||||||||
\(415\) | − | 7.71850i | − | 0.378886i | ||||||
\(416\) | −0.440552 | −0.0215998 | ||||||||
\(417\) | 5.76221 | 0.282176 | ||||||||
\(418\) | −1.07519 | −0.0525892 | ||||||||
\(419\) | 34.6712 | 1.69380 | 0.846900 | − | 0.531752i | \(-0.178466\pi\) | ||||
0.846900 | + | 0.531752i | \(0.178466\pi\) | |||||||
\(420\) | 4.44055i | 0.216677i | ||||||||
\(421\) | 23.1118i | 1.12640i | 0.826321 | + | 0.563200i | \(0.190430\pi\) | ||||
−0.826321 | + | 0.563200i | \(0.809570\pi\) | |||||||
\(422\) | 0.881103i | 0.0428914i | ||||||||
\(423\) | −10.8811 | −0.529057 | ||||||||
\(424\) | 2.44055i | 0.118524i | ||||||||
\(425\) | 4.83740i | 0.234648i | ||||||||
\(426\) | − | 9.67479i | − | 0.468745i | ||||||
\(427\) | 8.88110i | 0.429787i | ||||||||
\(428\) | −18.9248 | −0.914765 | ||||||||
\(429\) | − | 1.07519i | − | 0.0519106i | ||||||
\(430\) | − | 0.396844i | − | 0.0191375i | ||||||
\(431\) | 9.95629i | 0.479578i | 0.970825 | + | 0.239789i | \(0.0770782\pi\) | ||||
−0.970825 | + | 0.239789i | \(0.922922\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | −8.04371 | −0.386556 | −0.193278 | − | 0.981144i | \(-0.561912\pi\) | ||||
−0.193278 | + | 0.981144i | \(0.561912\pi\) | |||||||
\(434\) | −23.4370 | −1.12501 | ||||||||
\(435\) | 2.00000 | 0.0958927 | ||||||||
\(436\) | 12.0437i | 0.576789i | ||||||||
\(437\) | −1.25002 | −0.0597965 | ||||||||
\(438\) | 5.71850i | 0.273240i | ||||||||
\(439\) | 13.2779i | 0.633722i | 0.948472 | + | 0.316861i | \(0.102629\pi\) | ||||
−0.948472 | + | 0.316861i | \(0.897371\pi\) | |||||||
\(440\) | −2.44055 | −0.116349 | ||||||||
\(441\) | 12.7185 | 0.605643 | ||||||||
\(442\) | 2.13112i | 0.101367i | ||||||||
\(443\) | −2.41262 | −0.114627 | −0.0573136 | − | 0.998356i | \(-0.518253\pi\) | ||||
−0.0573136 | + | 0.998356i | \(0.518253\pi\) | |||||||
\(444\) | 0.198422 | + | 6.07953i | 0.00941669 | + | 0.288522i | ||||
\(445\) | −15.3217 | −0.726316 | ||||||||
\(446\) | 1.51574i | 0.0717724i | ||||||||
\(447\) | 1.60316 | 0.0758267 | ||||||||
\(448\) | 4.44055 | 0.209796 | ||||||||
\(449\) | − | 22.2465i | − | 1.04988i | −0.851141 | − | 0.524938i | \(-0.824089\pi\) | ||
0.851141 | − | 0.524938i | \(-0.175911\pi\) | |||||||
\(450\) | − | 1.00000i | − | 0.0471405i | ||||||
\(451\) | 4.88110 | 0.229842 | ||||||||
\(452\) | − | 2.00000i | − | 0.0940721i | ||||||
\(453\) | 4.28150 | 0.201162 | ||||||||
\(454\) | 14.5559 | 0.683142 | ||||||||
\(455\) | 1.95629 | 0.0917124 | ||||||||
\(456\) | −0.440552 | −0.0206307 | ||||||||
\(457\) | 20.5559i | 0.961564i | 0.876840 | + | 0.480782i | \(0.159647\pi\) | ||||
−0.876840 | + | 0.480782i | \(0.840353\pi\) | |||||||
\(458\) | 15.6748i | 0.732435i | ||||||||
\(459\) | − | 4.83740i | − | 0.225790i | ||||||
\(460\) | −2.83740 | −0.132294 | ||||||||
\(461\) | − | 12.6433i | − | 0.588858i | −0.955673 | − | 0.294429i | \(-0.904871\pi\) | ||
0.955673 | − | 0.294429i | \(-0.0951294\pi\) | |||||||
\(462\) | 10.8374i | 0.504201i | ||||||||
\(463\) | − | 32.4055i | − | 1.50601i | −0.658014 | − | 0.753006i | \(-0.728603\pi\) | ||
0.658014 | − | 0.753006i | \(-0.271397\pi\) | |||||||
\(464\) | − | 2.00000i | − | 0.0928477i | ||||||
\(465\) | 5.27795 | 0.244759 | ||||||||
\(466\) | − | 11.2779i | − | 0.522441i | ||||||
\(467\) | 26.5559i | 1.22886i | 0.788971 | + | 0.614430i | \(0.210614\pi\) | ||||
−0.788971 | + | 0.614430i | \(0.789386\pi\) | |||||||
\(468\) | − | 0.440552i | − | 0.0203645i | ||||||
\(469\) | 61.1118 | 2.82188 | ||||||||
\(470\) | 10.8811 | 0.501908 | ||||||||
\(471\) | 3.60316 | 0.166025 | ||||||||
\(472\) | 2.39684 | 0.110324 | ||||||||
\(473\) | − | 0.968518i | − | 0.0445325i | ||||||
\(474\) | −13.2779 | −0.609876 | ||||||||
\(475\) | 0.440552i | 0.0202139i | ||||||||
\(476\) | − | 21.4807i | − | 0.984567i | ||||||
\(477\) | −2.44055 | −0.111745 | ||||||||
\(478\) | −22.5559 | −1.03168 | ||||||||
\(479\) | 31.0122i | 1.41698i | 0.705718 | + | 0.708492i | \(0.250624\pi\) | ||||
−0.705718 | + | 0.708492i | \(0.749376\pi\) | |||||||
\(480\) | −1.00000 | −0.0456435 | ||||||||
\(481\) | 2.67835 | − | 0.0874152i | 0.122122 | − | 0.00398579i | ||||
\(482\) | −26.5559 | −1.20959 | ||||||||
\(483\) | 12.5996i | 0.573302i | ||||||||
\(484\) | 5.04371 | 0.229259 | ||||||||
\(485\) | 2.88110 | 0.130824 | ||||||||
\(486\) | 1.00000i | 0.0453609i | ||||||||
\(487\) | 7.20631i | 0.326549i | 0.986581 | + | 0.163275i | \(0.0522056\pi\) | ||||
−0.986581 | + | 0.163275i | \(0.947794\pi\) | |||||||
\(488\) | −2.00000 | −0.0905357 | ||||||||
\(489\) | − | 3.32165i | − | 0.150210i | ||||||
\(490\) | −12.7185 | −0.574563 | ||||||||
\(491\) | 2.44055 | 0.110141 | 0.0550703 | − | 0.998482i | \(-0.482462\pi\) | ||||
0.0550703 | + | 0.998482i | \(0.482462\pi\) | |||||||
\(492\) | 2.00000 | 0.0901670 | ||||||||
\(493\) | −9.67479 | −0.435731 | ||||||||
\(494\) | 0.194086i | 0.00873233i | ||||||||
\(495\) | − | 2.44055i | − | 0.109695i | ||||||
\(496\) | − | 5.27795i | − | 0.236987i | ||||||
\(497\) | 42.9614 | 1.92708 | ||||||||
\(498\) | − | 7.71850i | − | 0.345874i | ||||||
\(499\) | − | 36.7587i | − | 1.64554i | −0.568372 | − | 0.822772i | \(-0.692427\pi\) | ||
0.568372 | − | 0.822772i | \(-0.307573\pi\) | |||||||
\(500\) | 1.00000i | 0.0447214i | ||||||||
\(501\) | 2.83740i | 0.126765i | ||||||||
\(502\) | −3.27795 | −0.146302 | ||||||||
\(503\) | − | 29.1118i | − | 1.29803i | −0.760775 | − | 0.649015i | \(-0.775181\pi\) | ||
0.760775 | − | 0.649015i | \(-0.224819\pi\) | |||||||
\(504\) | 4.44055i | 0.197798i | ||||||||
\(505\) | − | 12.1591i | − | 0.541071i | ||||||
\(506\) | −6.92481 | −0.307845 | ||||||||
\(507\) | 12.8059 | 0.568731 | ||||||||
\(508\) | 7.55945 | 0.335396 | ||||||||
\(509\) | 6.90903 | 0.306237 | 0.153119 | − | 0.988208i | \(-0.451068\pi\) | ||||
0.153119 | + | 0.988208i | \(0.451068\pi\) | |||||||
\(510\) | 4.83740i | 0.214203i | ||||||||
\(511\) | −25.3933 | −1.12333 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | − | 0.440552i | − | 0.0194508i | ||||||
\(514\) | 20.0437 | 0.884090 | ||||||||
\(515\) | 10.5559 | 0.465148 | ||||||||
\(516\) | − | 0.396844i | − | 0.0174701i | ||||||
\(517\) | 26.5559 | 1.16793 | ||||||||
\(518\) | −26.9964 | + | 0.881103i | −1.18616 | + | 0.0387135i | ||||
\(519\) | −12.9964 | −0.570481 | ||||||||
\(520\) | 0.440552i | 0.0193195i | ||||||||
\(521\) | 40.5559 | 1.77679 | 0.888393 | − | 0.459084i | \(-0.151822\pi\) | ||||
0.888393 | + | 0.459084i | \(0.151822\pi\) | |||||||
\(522\) | 2.00000 | 0.0875376 | ||||||||
\(523\) | 42.4772i | 1.85740i | 0.370837 | + | 0.928698i | \(0.379071\pi\) | ||||
−0.370837 | + | 0.928698i | \(0.620929\pi\) | |||||||
\(524\) | − | 12.1591i | − | 0.531171i | ||||||
\(525\) | 4.44055 | 0.193802 | ||||||||
\(526\) | − | 17.4370i | − | 0.760289i | ||||||
\(527\) | −25.5315 | −1.11217 | ||||||||
\(528\) | −2.44055 | −0.106211 | ||||||||
\(529\) | 14.9492 | 0.649965 | ||||||||
\(530\) | 2.44055 | 0.106011 | ||||||||
\(531\) | 2.39684i | 0.104014i | ||||||||
\(532\) | − | 1.95629i | − | 0.0848160i | ||||||
\(533\) | − | 0.881103i | − | 0.0381648i | ||||||
\(534\) | −15.3217 | −0.663033 | ||||||||
\(535\) | 18.9248i | 0.818191i | ||||||||
\(536\) | 13.7622i | 0.594437i | ||||||||
\(537\) | − | 4.72205i | − | 0.203772i | ||||||
\(538\) | − | 16.4406i | − | 0.708803i | ||||||
\(539\) | −31.0402 | −1.33699 | ||||||||
\(540\) | − | 1.00000i | − | 0.0430331i | ||||||
\(541\) | 20.0437i | 0.861746i | 0.902413 | + | 0.430873i | \(0.141794\pi\) | ||||
−0.902413 | + | 0.430873i | \(0.858206\pi\) | |||||||
\(542\) | − | 24.3181i | − | 1.04455i | ||||||
\(543\) | 20.5559 | 0.882138 | ||||||||
\(544\) | 4.83740 | 0.207402 | ||||||||
\(545\) | 12.0437 | 0.515896 | ||||||||
\(546\) | 1.95629 | 0.0837216 | ||||||||
\(547\) | − | 20.1153i | − | 0.860070i | −0.902812 | − | 0.430035i | \(-0.858501\pi\) | ||
0.902812 | − | 0.430035i | \(-0.141499\pi\) | |||||||
\(548\) | −3.27795 | −0.140027 | ||||||||
\(549\) | − | 2.00000i | − | 0.0853579i | ||||||
\(550\) | 2.44055i | 0.104065i | ||||||||
\(551\) | −0.881103 | −0.0375363 | ||||||||
\(552\) | −2.83740 | −0.120768 | ||||||||
\(553\) | − | 58.9614i | − | 2.50729i | ||||||
\(554\) | 0.353137 | 0.0150033 | ||||||||
\(555\) | 6.07953 | − | 0.198422i | 0.258061 | − | 0.00842255i | ||||
\(556\) | −5.76221 | −0.244372 | ||||||||
\(557\) | − | 11.7622i | − | 0.498381i | −0.968455 | − | 0.249190i | \(-0.919836\pi\) | ||
0.968455 | − | 0.249190i | \(-0.0801645\pi\) | |||||||
\(558\) | 5.27795 | 0.223433 | ||||||||
\(559\) | −0.174830 | −0.00739453 | ||||||||
\(560\) | − | 4.44055i | − | 0.187648i | ||||||
\(561\) | 11.8059i | 0.498446i | ||||||||
\(562\) | −20.2028 | −0.852202 | ||||||||
\(563\) | − | 42.9614i | − | 1.81061i | −0.424765 | − | 0.905304i | \(-0.639643\pi\) | ||
0.424765 | − | 0.905304i | \(-0.360357\pi\) | |||||||
\(564\) | 10.8811 | 0.458177 | ||||||||
\(565\) | −2.00000 | −0.0841406 | ||||||||
\(566\) | −13.6469 | −0.573620 | ||||||||
\(567\) | −4.44055 | −0.186486 | ||||||||
\(568\) | 9.67479i | 0.405945i | ||||||||
\(569\) | − | 41.8775i | − | 1.75560i | −0.479029 | − | 0.877799i | \(-0.659011\pi\) | ||
0.479029 | − | 0.877799i | \(-0.340989\pi\) | |||||||
\(570\) | 0.440552i | 0.0184527i | ||||||||
\(571\) | −37.7622 | −1.58030 | −0.790150 | − | 0.612914i | \(-0.789997\pi\) | ||||
−0.790150 | + | 0.612914i | \(0.789997\pi\) | |||||||
\(572\) | 1.07519i | 0.0449559i | ||||||||
\(573\) | 9.16260i | 0.382773i | ||||||||
\(574\) | 8.88110i | 0.370690i | ||||||||
\(575\) | 2.83740i | 0.118328i | ||||||||
\(576\) | −1.00000 | −0.0416667 | ||||||||
\(577\) | − | 2.56300i | − | 0.106699i | −0.998576 | − | 0.0533496i | \(-0.983010\pi\) | ||
0.998576 | − | 0.0533496i | \(-0.0169898\pi\) | |||||||
\(578\) | − | 6.40040i | − | 0.266221i | ||||||
\(579\) | − | 14.8811i | − | 0.618438i | ||||||
\(580\) | −2.00000 | −0.0830455 | ||||||||
\(581\) | 34.2744 | 1.42194 | ||||||||
\(582\) | 2.88110 | 0.119426 | ||||||||
\(583\) | 5.95629 | 0.246684 | ||||||||
\(584\) | − | 5.71850i | − | 0.236633i | ||||||
\(585\) | −0.440552 | −0.0182146 | ||||||||
\(586\) | − | 6.44055i | − | 0.266057i | ||||||
\(587\) | − | 45.1992i | − | 1.86557i | −0.360432 | − | 0.932785i | \(-0.617371\pi\) | ||
0.360432 | − | 0.932785i | \(-0.382629\pi\) | |||||||
\(588\) | −12.7185 | −0.524502 | ||||||||
\(589\) | −2.32521 | −0.0958085 | ||||||||
\(590\) | − | 2.39684i | − | 0.0986765i | ||||||
\(591\) | −9.55945 | −0.393223 | ||||||||
\(592\) | −0.198422 | − | 6.07953i | −0.00815510 | − | 0.249867i | ||||
\(593\) | 43.5086 | 1.78669 | 0.893343 | − | 0.449376i | \(-0.148354\pi\) | ||||
0.893343 | + | 0.449376i | \(0.148354\pi\) | |||||||
\(594\) | − | 2.44055i | − | 0.100137i | ||||||
\(595\) | −21.4807 | −0.880623 | ||||||||
\(596\) | −1.60316 | −0.0656678 | ||||||||
\(597\) | − | 20.4843i | − | 0.838365i | ||||||
\(598\) | 1.25002i | 0.0511171i | ||||||||
\(599\) | 26.6433 | 1.08862 | 0.544308 | − | 0.838885i | \(-0.316792\pi\) | ||||
0.544308 | + | 0.838885i | \(0.316792\pi\) | |||||||
\(600\) | 1.00000i | 0.0408248i | ||||||||
\(601\) | 0.924811 | 0.0377238 | 0.0188619 | − | 0.999822i | \(-0.493996\pi\) | ||||
0.0188619 | + | 0.999822i | \(0.493996\pi\) | |||||||
\(602\) | 1.76221 | 0.0718222 | ||||||||
\(603\) | −13.7622 | −0.560440 | ||||||||
\(604\) | −4.28150 | −0.174212 | ||||||||
\(605\) | − | 5.04371i | − | 0.205056i | ||||||
\(606\) | − | 12.1591i | − | 0.493928i | ||||||
\(607\) | − | 2.55589i | − | 0.103741i | −0.998654 | − | 0.0518703i | \(-0.983482\pi\) | ||
0.998654 | − | 0.0518703i | \(-0.0165182\pi\) | |||||||
\(608\) | 0.440552 | 0.0178667 | ||||||||
\(609\) | 8.88110i | 0.359880i | ||||||||
\(610\) | 2.00000i | 0.0809776i | ||||||||
\(611\) | − | 4.79369i | − | 0.193932i | ||||||
\(612\) | 4.83740i | 0.195540i | ||||||||
\(613\) | 10.1591 | 0.410320 | 0.205160 | − | 0.978728i | \(-0.434228\pi\) | ||||
0.205160 | + | 0.978728i | \(0.434228\pi\) | |||||||
\(614\) | − | 20.3181i | − | 0.819972i | ||||||
\(615\) | − | 2.00000i | − | 0.0806478i | ||||||
\(616\) | − | 10.8374i | − | 0.436651i | ||||||
\(617\) | −12.1591 | −0.489505 | −0.244752 | − | 0.969586i | \(-0.578707\pi\) | ||||
−0.244752 | + | 0.969586i | \(0.578707\pi\) | |||||||
\(618\) | 10.5559 | 0.424620 | ||||||||
\(619\) | 23.5244 | 0.945526 | 0.472763 | − | 0.881190i | \(-0.343257\pi\) | ||||
0.472763 | + | 0.881190i | \(0.343257\pi\) | |||||||
\(620\) | −5.27795 | −0.211967 | ||||||||
\(621\) | − | 2.83740i | − | 0.113861i | ||||||
\(622\) | 6.23779 | 0.250113 | ||||||||
\(623\) | − | 68.0366i | − | 2.72583i | ||||||
\(624\) | 0.440552i | 0.0176362i | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −8.55589 | −0.341962 | ||||||||
\(627\) | 1.07519i | 0.0429389i | ||||||||
\(628\) | −3.60316 | −0.143782 | ||||||||
\(629\) | −29.4091 | + | 0.959846i | −1.17262 | + | 0.0382716i | ||||
\(630\) | 4.44055 | 0.176916 | ||||||||
\(631\) | 3.60316i | 0.143439i | 0.997425 | + | 0.0717197i | \(0.0228487\pi\) | ||||
−0.997425 | + | 0.0717197i | \(0.977151\pi\) | |||||||
\(632\) | 13.2779 | 0.528168 | ||||||||
\(633\) | 0.881103 | 0.0350207 | ||||||||
\(634\) | − | 33.5960i | − | 1.33427i | ||||||
\(635\) | − | 7.55945i | − | 0.299988i | ||||||
\(636\) | 2.44055 | 0.0967742 | ||||||||
\(637\) | 5.60316i | 0.222005i | ||||||||
\(638\) | −4.88110 | −0.193245 | ||||||||
\(639\) | −9.67479 | −0.382729 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | −37.4370 | −1.47867 | −0.739336 | − | 0.673336i | \(-0.764861\pi\) | ||||
−0.739336 | + | 0.673336i | \(0.764861\pi\) | |||||||
\(642\) | 18.9248i | 0.746903i | ||||||||
\(643\) | − | 0.678345i | − | 0.0267513i | −0.999911 | − | 0.0133757i | \(-0.995742\pi\) | ||
0.999911 | − | 0.0133757i | \(-0.00425773\pi\) | |||||||
\(644\) | − | 12.5996i | − | 0.496494i | ||||||
\(645\) | −0.396844 | −0.0156257 | ||||||||
\(646\) | − | 2.13112i | − | 0.0838479i | ||||||
\(647\) | − | 6.92481i | − | 0.272242i | −0.990692 | − | 0.136121i | \(-0.956536\pi\) | ||
0.990692 | − | 0.136121i | \(-0.0434637\pi\) | |||||||
\(648\) | − | 1.00000i | − | 0.0392837i | ||||||
\(649\) | − | 5.84962i | − | 0.229618i | ||||||
\(650\) | 0.440552 | 0.0172799 | ||||||||
\(651\) | 23.4370i | 0.918568i | ||||||||
\(652\) | 3.32165i | 0.130086i | ||||||||
\(653\) | 15.4441i | 0.604375i | 0.953249 | + | 0.302187i | \(0.0977168\pi\) | ||||
−0.953249 | + | 0.302187i | \(0.902283\pi\) | |||||||
\(654\) | 12.0437 | 0.470946 | ||||||||
\(655\) | −12.1591 | −0.475093 | ||||||||
\(656\) | −2.00000 | −0.0780869 | ||||||||
\(657\) | 5.71850 | 0.223100 | ||||||||
\(658\) | 48.3181i | 1.88364i | ||||||||
\(659\) | −18.9527 | −0.738294 | −0.369147 | − | 0.929371i | \(-0.620350\pi\) | ||||
−0.369147 | + | 0.929371i | \(0.620350\pi\) | |||||||
\(660\) | 2.44055i | 0.0949983i | ||||||||
\(661\) | − | 36.3618i | − | 1.41431i | −0.707058 | − | 0.707155i | \(-0.749978\pi\) | ||
0.707058 | − | 0.707155i | \(-0.250022\pi\) | |||||||
\(662\) | 31.2779 | 1.21565 | ||||||||
\(663\) | 2.13112 | 0.0827659 | ||||||||
\(664\) | 7.71850i | 0.299536i | ||||||||
\(665\) | −1.95629 | −0.0758618 | ||||||||
\(666\) | 6.07953 | − | 0.198422i | 0.235577 | − | 0.00768870i | ||||
\(667\) | −5.67479 | −0.219729 | ||||||||
\(668\) | − | 2.83740i | − | 0.109782i | ||||||
\(669\) | 1.51574 | 0.0586019 | ||||||||
\(670\) | 13.7622 | 0.531680 | ||||||||
\(671\) | 4.88110i | 0.188433i | ||||||||
\(672\) | − | 4.44055i | − | 0.171298i | ||||||
\(673\) | 9.80591 | 0.377990 | 0.188995 | − | 0.981978i | \(-0.439477\pi\) | ||||
0.188995 | + | 0.981978i | \(0.439477\pi\) | |||||||
\(674\) | − | 5.63108i | − | 0.216901i | ||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | −12.8059 | −0.492535 | ||||||||
\(677\) | 28.2902 | 1.08728 | 0.543640 | − | 0.839319i | \(-0.317046\pi\) | ||||
0.543640 | + | 0.839319i | \(0.317046\pi\) | |||||||
\(678\) | −2.00000 | −0.0768095 | ||||||||
\(679\) | 12.7937i | 0.490977i | ||||||||
\(680\) | − | 4.83740i | − | 0.185506i | ||||||
\(681\) | − | 14.5559i | − | 0.557783i | ||||||
\(682\) | −12.8811 | −0.493243 | ||||||||
\(683\) | − | 24.3181i | − | 0.930506i | −0.885178 | − | 0.465253i | \(-0.845963\pi\) | ||
0.885178 | − | 0.465253i | \(-0.154037\pi\) | |||||||
\(684\) | 0.440552i | 0.0168449i | ||||||||
\(685\) | 3.27795i | 0.125244i | ||||||||
\(686\) | − | 25.3933i | − | 0.969520i | ||||||
\(687\) | 15.6748 | 0.598031 | ||||||||
\(688\) | 0.396844i | 0.0151295i | ||||||||
\(689\) | − | 1.07519i | − | 0.0409614i | ||||||
\(690\) | 2.83740i | 0.108018i | ||||||||
\(691\) | 5.53152 | 0.210429 | 0.105214 | − | 0.994450i | \(-0.466447\pi\) | ||||
0.105214 | + | 0.994450i | \(0.466447\pi\) | |||||||
\(692\) | 12.9964 | 0.494051 | ||||||||
\(693\) | 10.8374 | 0.411679 | ||||||||
\(694\) | 0.881103 | 0.0334462 | ||||||||
\(695\) | 5.76221i | 0.218573i | ||||||||
\(696\) | −2.00000 | −0.0758098 | ||||||||
\(697\) | 9.67479i | 0.366459i | ||||||||
\(698\) | 0.555895i | 0.0210409i | ||||||||
\(699\) | −11.2779 | −0.426571 | ||||||||
\(700\) | −4.44055 | −0.167837 | ||||||||
\(701\) | − | 23.6748i | − | 0.894185i | −0.894488 | − | 0.447092i | \(-0.852460\pi\) | ||
0.894488 | − | 0.447092i | \(-0.147540\pi\) | |||||||
\(702\) | −0.440552 | −0.0166276 | ||||||||
\(703\) | −2.67835 | + | 0.0874152i | −0.101016 | + | 0.00329693i | ||||
\(704\) | 2.44055 | 0.0919818 | ||||||||
\(705\) | − | 10.8811i | − | 0.409806i | ||||||
\(706\) | −5.20631 | −0.195942 | ||||||||
\(707\) | 53.9929 | 2.03061 | ||||||||
\(708\) | − | 2.39684i | − | 0.0900789i | ||||||
\(709\) | 3.07519i | 0.115491i | 0.998331 | + | 0.0577456i | \(0.0183912\pi\) | ||||
−0.998331 | + | 0.0577456i | \(0.981609\pi\) | |||||||
\(710\) | 9.67479 | 0.363088 | ||||||||
\(711\) | 13.2779i | 0.497962i | ||||||||
\(712\) | 15.3217 | 0.574203 | ||||||||
\(713\) | −14.9756 | −0.560842 | ||||||||
\(714\) | −21.4807 | −0.803895 | ||||||||
\(715\) | 1.07519 | 0.0402098 | ||||||||
\(716\) | 4.72205i | 0.176471i | ||||||||
\(717\) | 22.5559i | 0.842365i | ||||||||
\(718\) | − | 15.4370i | − | 0.576104i | ||||||
\(719\) | −31.3496 | −1.16914 | −0.584571 | − | 0.811342i | \(-0.698737\pi\) | ||||
−0.584571 | + | 0.811342i | \(0.698737\pi\) | |||||||
\(720\) | 1.00000i | 0.0372678i | ||||||||
\(721\) | 46.8740i | 1.74568i | ||||||||
\(722\) | 18.8059i | 0.699884i | ||||||||
\(723\) | 26.5559i | 0.987624i | ||||||||
\(724\) | −20.5559 | −0.763954 | ||||||||
\(725\) | 2.00000i | 0.0742781i | ||||||||
\(726\) | − | 5.04371i | − | 0.187190i | ||||||
\(727\) | − | 20.0874i | − | 0.745001i | −0.928032 | − | 0.372500i | \(-0.878500\pi\) | ||
0.928032 | − | 0.372500i | \(-0.121500\pi\) | |||||||
\(728\) | −1.95629 | −0.0725050 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −5.71850 | −0.211651 | ||||||||
\(731\) | 1.91969 | 0.0710024 | ||||||||
\(732\) | 2.00000i | 0.0739221i | ||||||||
\(733\) | 7.83384 | 0.289350 | 0.144675 | − | 0.989479i | \(-0.453786\pi\) | ||||
0.144675 | + | 0.989479i | \(0.453786\pi\) | |||||||
\(734\) | − | 14.9964i | − | 0.553529i | ||||||
\(735\) | 12.7185i | 0.469129i | ||||||||
\(736\) | 2.83740 | 0.104588 | ||||||||
\(737\) | 33.5874 | 1.23721 | ||||||||
\(738\) | − | 2.00000i | − | 0.0736210i | ||||||
\(739\) | −52.6362 | −1.93625 | −0.968127 | − | 0.250460i | \(-0.919418\pi\) | ||||
−0.968127 | + | 0.250460i | \(0.919418\pi\) | |||||||
\(740\) | −6.07953 | + | 0.198422i | −0.223488 | + | 0.00729414i | ||||
\(741\) | 0.194086 | 0.00712992 | ||||||||
\(742\) | 10.8374i | 0.397853i | ||||||||
\(743\) | −8.55589 | −0.313885 | −0.156943 | − | 0.987608i | \(-0.550164\pi\) | ||||
−0.156943 | + | 0.987608i | \(0.550164\pi\) | |||||||
\(744\) | −5.27795 | −0.193499 | ||||||||
\(745\) | 1.60316i | 0.0587351i | ||||||||
\(746\) | 33.5086i | 1.22684i | ||||||||
\(747\) | −7.71850 | −0.282405 | ||||||||
\(748\) | − | 11.8059i | − | 0.431667i | ||||||
\(749\) | −84.0366 | −3.07063 | ||||||||
\(750\) | 1.00000 | 0.0365148 | ||||||||
\(751\) | 16.0000 | 0.583848 | 0.291924 | − | 0.956441i | \(-0.405705\pi\) | ||||
0.291924 | + | 0.956441i | \(0.405705\pi\) | |||||||
\(752\) | −10.8811 | −0.396793 | ||||||||
\(753\) | 3.27795i | 0.119455i | ||||||||
\(754\) | 0.881103i | 0.0320879i | ||||||||
\(755\) | 4.28150i | 0.155820i | ||||||||
\(756\) | 4.44055 | 0.161501 | ||||||||
\(757\) | 39.4020i | 1.43209i | 0.698055 | + | 0.716044i | \(0.254049\pi\) | ||||
−0.698055 | + | 0.716044i | \(0.745951\pi\) | |||||||
\(758\) | 34.6433i | 1.25830i | ||||||||
\(759\) | 6.92481i | 0.251355i | ||||||||
\(760\) | − | 0.440552i | − | 0.0159805i | ||||||
\(761\) | −40.5559 | −1.47015 | −0.735075 | − | 0.677986i | \(-0.762853\pi\) | ||||
−0.735075 | + | 0.677986i | \(0.762853\pi\) | |||||||
\(762\) | − | 7.55945i | − | 0.273850i | ||||||
\(763\) | 53.4807i | 1.93613i | ||||||||
\(764\) | − | 9.16260i | − | 0.331491i | ||||||
\(765\) | 4.83740 | 0.174896 | ||||||||
\(766\) | 8.51219 | 0.307558 | ||||||||
\(767\) | −1.05593 | −0.0381276 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | − | 4.08742i | − | 0.147396i | −0.997281 | − | 0.0736980i | \(-0.976520\pi\) | ||
0.997281 | − | 0.0736980i | \(-0.0234801\pi\) | |||||||
\(770\) | −10.8374 | −0.390553 | ||||||||
\(771\) | − | 20.0437i | − | 0.721856i | ||||||
\(772\) | 14.8811i | 0.535583i | ||||||||
\(773\) | 24.6783 | 0.887618 | 0.443809 | − | 0.896121i | \(-0.353627\pi\) | ||||
0.443809 | + | 0.896121i | \(0.353627\pi\) | |||||||
\(774\) | −0.396844 | −0.0142643 | ||||||||
\(775\) | 5.27795i | 0.189589i | ||||||||
\(776\) | −2.88110 | −0.103426 | ||||||||
\(777\) | 0.881103 | + | 26.9964i | 0.0316094 | + | 0.968492i | ||||
\(778\) | 27.6748 | 0.992189 | ||||||||
\(779\) | 0.881103i | 0.0315688i | ||||||||
\(780\) | 0.440552 | 0.0157743 | ||||||||
\(781\) | 23.6118 | 0.844898 | ||||||||
\(782\) | − | 13.7256i | − | 0.490827i | ||||||
\(783\) | − | 2.00000i | − | 0.0714742i | ||||||
\(784\) | 12.7185 | 0.454232 | ||||||||
\(785\) | 3.60316i | 0.128602i | ||||||||
\(786\) | −12.1591 | −0.433699 | ||||||||
\(787\) | −37.1992 | −1.32601 | −0.663004 | − | 0.748616i | \(-0.730719\pi\) | ||||
−0.663004 | + | 0.748616i | \(0.730719\pi\) | |||||||
\(788\) | 9.55945 | 0.340541 | ||||||||
\(789\) | −17.4370 | −0.620774 | ||||||||
\(790\) | − | 13.2779i | − | 0.472408i | ||||||
\(791\) | − | 8.88110i | − | 0.315776i | ||||||
\(792\) | 2.44055i | 0.0867212i | ||||||||
\(793\) | 0.881103 | 0.0312889 | ||||||||
\(794\) | 9.36536i | 0.332364i | ||||||||
\(795\) | − | 2.44055i | − | 0.0865574i | ||||||
\(796\) | 20.4843i | 0.726045i | ||||||||
\(797\) | 15.8496i | 0.561422i | 0.959792 | + | 0.280711i | \(0.0905703\pi\) | ||||
−0.959792 | + | 0.280711i | \(0.909430\pi\) | |||||||
\(798\) | −1.95629 | −0.0692520 | ||||||||
\(799\) | 52.6362i | 1.86214i | ||||||||
\(800\) | − | 1.00000i | − | 0.0353553i | ||||||
\(801\) | 15.3217i | 0.541364i | ||||||||
\(802\) | 7.88466 | 0.278417 | ||||||||
\(803\) | −13.9563 | −0.492507 | ||||||||
\(804\) | 13.7622 | 0.485356 | ||||||||
\(805\) | −12.5996 | −0.444078 | ||||||||
\(806\) | 2.32521i | 0.0819020i | ||||||||
\(807\) | −16.4406 | −0.578735 | ||||||||
\(808\) | 12.1591i | 0.427754i | ||||||||
\(809\) | 53.0839i | 1.86633i | 0.359449 | + | 0.933165i | \(0.382965\pi\) | ||||
−0.359449 | + | 0.933165i | \(0.617035\pi\) | |||||||
\(810\) | −1.00000 | −0.0351364 | ||||||||
\(811\) | 26.6433 | 0.935573 | 0.467787 | − | 0.883841i | \(-0.345052\pi\) | ||||
0.467787 | + | 0.883841i | \(0.345052\pi\) | |||||||
\(812\) | − | 8.88110i | − | 0.311666i | ||||||
\(813\) | −24.3181 | −0.852873 | ||||||||
\(814\) | −14.8374 | + | 0.484259i | −0.520050 | + | 0.0169733i | ||||
\(815\) | 3.32165 | 0.116352 | ||||||||
\(816\) | − | 4.83740i | − | 0.169343i | ||||||
\(817\) | 0.174830 | 0.00611654 | ||||||||
\(818\) | 38.7307 | 1.35419 | ||||||||
\(819\) | − | 1.95629i | − | 0.0683584i | ||||||
\(820\) | 2.00000i | 0.0698430i | ||||||||
\(821\) | −22.9090 | −0.799531 | −0.399765 | − | 0.916618i | \(-0.630908\pi\) | ||||
−0.399765 | + | 0.916618i | \(0.630908\pi\) | |||||||
\(822\) | 3.27795i | 0.114332i | ||||||||
\(823\) | 40.1082 | 1.39809 | 0.699043 | − | 0.715080i | \(-0.253610\pi\) | ||||
0.699043 | + | 0.715080i | \(0.253610\pi\) | |||||||
\(824\) | −10.5559 | −0.367732 | ||||||||
\(825\) | 2.44055 | 0.0849691 | ||||||||
\(826\) | 10.6433 | 0.370328 | ||||||||
\(827\) | 9.67479i | 0.336425i | 0.985751 | + | 0.168213i | \(0.0537996\pi\) | ||||
−0.985751 | + | 0.168213i | \(0.946200\pi\) | |||||||
\(828\) | 2.83740i | 0.0986063i | ||||||||
\(829\) | 12.0437i | 0.418295i | 0.977884 | + | 0.209148i | \(0.0670689\pi\) | ||||
−0.977884 | + | 0.209148i | \(0.932931\pi\) | |||||||
\(830\) | 7.71850 | 0.267913 | ||||||||
\(831\) | − | 0.353137i | − | 0.0122502i | ||||||
\(832\) | − | 0.440552i | − | 0.0152734i | ||||||
\(833\) | − | 61.5244i | − | 2.13169i | ||||||
\(834\) | 5.76221i | 0.199529i | ||||||||
\(835\) | −2.83740 | −0.0981921 | ||||||||
\(836\) | − | 1.07519i | − | 0.0371862i | ||||||
\(837\) | − | 5.27795i | − | 0.182433i | ||||||
\(838\) | 34.6712i | 1.19770i | ||||||||
\(839\) | 3.68190 | 0.127113 | 0.0635566 | − | 0.997978i | \(-0.479756\pi\) | ||||
0.0635566 | + | 0.997978i | \(0.479756\pi\) | |||||||
\(840\) | −4.44055 | −0.153214 | ||||||||
\(841\) | 25.0000 | 0.862069 | ||||||||
\(842\) | −23.1118 | −0.796485 | ||||||||
\(843\) | 20.2028i | 0.695820i | ||||||||
\(844\) | −0.881103 | −0.0303288 | ||||||||
\(845\) | 12.8059i | 0.440537i | ||||||||
\(846\) | − | 10.8811i | − | 0.374100i | ||||||
\(847\) | 22.3968 | 0.769565 | ||||||||
\(848\) | −2.44055 | −0.0838089 | ||||||||
\(849\) | 13.6469i | 0.468359i | ||||||||
\(850\) | −4.83740 | −0.165921 | ||||||||
\(851\) | −17.2500 | + | 0.563002i | −0.591323 | + | 0.0192995i | ||||
\(852\) | 9.67479 | 0.331453 | ||||||||
\(853\) | − | 17.8847i | − | 0.612359i | −0.951974 | − | 0.306179i | \(-0.900949\pi\) | ||
0.951974 | − | 0.306179i | \(-0.0990508\pi\) | |||||||
\(854\) | −8.88110 | −0.303905 | ||||||||
\(855\) | 0.440552 | 0.0150665 | ||||||||
\(856\) | − | 18.9248i | − | 0.646837i | ||||||
\(857\) | 33.1555i | 1.13257i | 0.824209 | + | 0.566285i | \(0.191620\pi\) | ||||
−0.824209 | + | 0.566285i | \(0.808380\pi\) | |||||||
\(858\) | 1.07519 | 0.0367064 | ||||||||
\(859\) | 13.4091i | 0.457512i | 0.973484 | + | 0.228756i | \(0.0734657\pi\) | ||||
−0.973484 | + | 0.228756i | \(0.926534\pi\) | |||||||
\(860\) | 0.396844 | 0.0135323 | ||||||||
\(861\) | 8.88110 | 0.302667 | ||||||||
\(862\) | −9.95629 | −0.339113 | ||||||||
\(863\) | −3.35669 | −0.114263 | −0.0571315 | − | 0.998367i | \(-0.518195\pi\) | ||||
−0.0571315 | + | 0.998367i | \(0.518195\pi\) | |||||||
\(864\) | 1.00000i | 0.0340207i | ||||||||
\(865\) | − | 12.9964i | − | 0.441892i | ||||||
\(866\) | − | 8.04371i | − | 0.273336i | ||||||
\(867\) | −6.40040 | −0.217369 | ||||||||
\(868\) | − | 23.4370i | − | 0.795504i | ||||||
\(869\) | − | 32.4055i | − | 1.09928i | ||||||
\(870\) | 2.00000i | 0.0678064i | ||||||||
\(871\) | − | 6.06296i | − | 0.205436i | ||||||
\(872\) | −12.0437 | −0.407851 | ||||||||
\(873\) | − | 2.88110i | − | 0.0975106i | ||||||
\(874\) | − | 1.25002i | − | 0.0422825i | ||||||
\(875\) | 4.44055i | 0.150118i | ||||||||
\(876\) | −5.71850 | −0.193210 | ||||||||
\(877\) | −14.9527 | −0.504918 | −0.252459 | − | 0.967608i | \(-0.581239\pi\) | ||||
−0.252459 | + | 0.967608i | \(0.581239\pi\) | |||||||
\(878\) | −13.2779 | −0.448109 | ||||||||
\(879\) | −6.44055 | −0.217234 | ||||||||
\(880\) | − | 2.44055i | − | 0.0822710i | ||||||
\(881\) | 54.6362 | 1.84074 | 0.920370 | − | 0.391048i | \(-0.127887\pi\) | ||||
0.920370 | + | 0.391048i | \(0.127887\pi\) | |||||||
\(882\) | 12.7185i | 0.428254i | ||||||||
\(883\) | − | 50.0524i | − | 1.68440i | −0.539168 | − | 0.842198i | \(-0.681261\pi\) | ||
0.539168 | − | 0.842198i | \(-0.318739\pi\) | |||||||
\(884\) | −2.13112 | −0.0716774 | ||||||||
\(885\) | −2.39684 | −0.0805690 | ||||||||
\(886\) | − | 2.41262i | − | 0.0810537i | ||||||
\(887\) | −27.0244 | −0.907390 | −0.453695 | − | 0.891157i | \(-0.649894\pi\) | ||||
−0.453695 | + | 0.891157i | \(0.649894\pi\) | |||||||
\(888\) | −6.07953 | + | 0.198422i | −0.204016 | + | 0.00665861i | ||||
\(889\) | 33.5681 | 1.12584 | ||||||||
\(890\) | − | 15.3217i | − | 0.513583i | ||||||
\(891\) | −2.44055 | −0.0817616 | ||||||||
\(892\) | −1.51574 | −0.0507508 | ||||||||
\(893\) | 4.79369i | 0.160415i | ||||||||
\(894\) | 1.60316i | 0.0536176i | ||||||||
\(895\) | 4.72205 | 0.157841 | ||||||||
\(896\) | 4.44055i | 0.148348i | ||||||||
\(897\) | 1.25002 | 0.0417369 | ||||||||
\(898\) | 22.2465 | 0.742374 | ||||||||
\(899\) | −10.5559 | −0.352059 | ||||||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | 11.8059i | 0.393312i | ||||||||
\(902\) | 4.88110i | 0.162523i | ||||||||
\(903\) | − | 1.76221i | − | 0.0586426i | ||||||
\(904\) | 2.00000 | 0.0665190 | ||||||||
\(905\) | 20.5559i | 0.683301i | ||||||||
\(906\) | 4.28150i | 0.142243i | ||||||||
\(907\) | − | 12.0279i | − | 0.399381i | −0.979859 | − | 0.199690i | \(-0.936006\pi\) | ||
0.979859 | − | 0.199690i | \(-0.0639936\pi\) | |||||||
\(908\) | 14.5559i | 0.483054i | ||||||||
\(909\) | −12.1591 | −0.403290 | ||||||||
\(910\) | 1.95629i | 0.0648505i | ||||||||
\(911\) | 24.0000i | 0.795155i | 0.917568 | + | 0.397578i | \(0.130149\pi\) | ||||
−0.917568 | + | 0.397578i | \(0.869851\pi\) | |||||||
\(912\) | − | 0.440552i | − | 0.0145881i | ||||||
\(913\) | 18.8374 | 0.623427 | ||||||||
\(914\) | −20.5559 | −0.679929 | ||||||||
\(915\) | 2.00000 | 0.0661180 | ||||||||
\(916\) | −15.6748 | −0.517910 | ||||||||
\(917\) | − | 53.9929i | − | 1.78300i | ||||||
\(918\) | 4.83740 | 0.159658 | ||||||||
\(919\) | 23.1276i | 0.762908i | 0.924388 | + | 0.381454i | \(0.124577\pi\) | ||||
−0.924388 | + | 0.381454i | \(0.875423\pi\) | |||||||
\(920\) | − | 2.83740i | − | 0.0935462i | ||||||
\(921\) | −20.3181 | −0.669504 | ||||||||
\(922\) | 12.6433 | 0.416385 | ||||||||
\(923\) | − | 4.26225i | − | 0.140294i | ||||||
\(924\) | −10.8374 | −0.356524 | ||||||||
\(925\) | 0.198422 | + | 6.07953i | 0.00652408 | + | 0.199894i | ||||
\(926\) | 32.4055 | 1.06491 | ||||||||
\(927\) | − | 10.5559i | − | 0.346701i | ||||||
\(928\) | 2.00000 | 0.0656532 | ||||||||
\(929\) | 12.3252 | 0.404377 | 0.202188 | − | 0.979347i | \(-0.435195\pi\) | ||||
0.202188 | + | 0.979347i | \(0.435195\pi\) | |||||||
\(930\) | 5.27795i | 0.173071i | ||||||||
\(931\) | − | 5.60316i | − | 0.183636i | ||||||
\(932\) | 11.2779 | 0.369421 | ||||||||
\(933\) | − | 6.23779i | − | 0.204216i | ||||||
\(934\) | −26.5559 | −0.868935 | ||||||||
\(935\) | −11.8059 | −0.386095 | ||||||||
\(936\) | 0.440552 | 0.0143999 | ||||||||
\(937\) | −24.2378 | −0.791814 | −0.395907 | − | 0.918291i | \(-0.629570\pi\) | ||||
−0.395907 | + | 0.918291i | \(0.629570\pi\) | |||||||
\(938\) | 61.1118i | 1.99537i | ||||||||
\(939\) | 8.55589i | 0.279211i | ||||||||
\(940\) | 10.8811i | 0.354902i | ||||||||
\(941\) | −42.2394 | −1.37696 | −0.688482 | − | 0.725254i | \(-0.741723\pi\) | ||||
−0.688482 | + | 0.725254i | \(0.741723\pi\) | |||||||
\(942\) | 3.60316i | 0.117397i | ||||||||
\(943\) | 5.67479i | 0.184797i | ||||||||
\(944\) | 2.39684i | 0.0780106i | ||||||||
\(945\) | − | 4.44055i | − | 0.144451i | ||||||
\(946\) | 0.968518 | 0.0314893 | ||||||||
\(947\) | 11.5244i | 0.374493i | 0.982313 | + | 0.187247i | \(0.0599563\pi\) | ||||
−0.982313 | + | 0.187247i | \(0.940044\pi\) | |||||||
\(948\) | − | 13.2779i | − | 0.431248i | ||||||
\(949\) | 2.51929i | 0.0817798i | ||||||||
\(950\) | −0.440552 | −0.0142934 | ||||||||
\(951\) | −33.5960 | −1.08943 | ||||||||
\(952\) | 21.4807 | 0.696194 | ||||||||
\(953\) | 6.30943 | 0.204382 | 0.102191 | − | 0.994765i | \(-0.467415\pi\) | ||||
0.102191 | + | 0.994765i | \(0.467415\pi\) | |||||||
\(954\) | − | 2.44055i | − | 0.0790158i | ||||||
\(955\) | −9.16260 | −0.296495 | ||||||||
\(956\) | − | 22.5559i | − | 0.729510i | ||||||
\(957\) | 4.88110i | 0.157784i | ||||||||
\(958\) | −31.0122 | −1.00196 | ||||||||
\(959\) | −14.5559 | −0.470034 | ||||||||
\(960\) | − | 1.00000i | − | 0.0322749i | ||||||
\(961\) | 3.14327 | 0.101396 | ||||||||
\(962\) | 0.0874152 | + | 2.67835i | 0.00281838 | + | 0.0863533i | ||||
\(963\) | 18.9248 | 0.609844 | ||||||||
\(964\) | − | 26.5559i | − | 0.855308i | ||||||
\(965\) | 14.8811 | 0.479040 | ||||||||
\(966\) | −12.5996 | −0.405386 | ||||||||
\(967\) | 14.4126i | 0.463479i | 0.972778 | + | 0.231739i | \(0.0744417\pi\) | ||||
−0.972778 | + | 0.231739i | \(0.925558\pi\) | |||||||
\(968\) | 5.04371i | 0.162111i | ||||||||
\(969\) | −2.13112 | −0.0684615 | ||||||||
\(970\) | 2.88110i | 0.0925067i | ||||||||
\(971\) | −48.3968 | −1.55313 | −0.776564 | − | 0.630038i | \(-0.783039\pi\) | ||||
−0.776564 | + | 0.630038i | \(0.783039\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | −25.5874 | −0.820294 | ||||||||
\(974\) | −7.20631 | −0.230905 | ||||||||
\(975\) | − | 0.440552i | − | 0.0141089i | ||||||
\(976\) | − | 2.00000i | − | 0.0640184i | ||||||
\(977\) | 44.0437i | 1.40908i | 0.709663 | + | 0.704542i | \(0.248847\pi\) | ||||
−0.709663 | + | 0.704542i | \(0.751153\pi\) | |||||||
\(978\) | 3.32165 | 0.106215 | ||||||||
\(979\) | − | 37.3933i | − | 1.19509i | ||||||
\(980\) | − | 12.7185i | − | 0.406278i | ||||||
\(981\) | − | 12.0437i | − | 0.384526i | ||||||
\(982\) | 2.44055i | 0.0778811i | ||||||||
\(983\) | 0.468480 | 0.0149422 | 0.00747109 | − | 0.999972i | \(-0.497622\pi\) | ||||
0.00747109 | + | 0.999972i | \(0.497622\pi\) | |||||||
\(984\) | 2.00000i | 0.0637577i | ||||||||
\(985\) | − | 9.55945i | − | 0.304589i | ||||||
\(986\) | − | 9.67479i | − | 0.308108i | ||||||
\(987\) | 48.3181 | 1.53798 | ||||||||
\(988\) | −0.194086 | −0.00617469 | ||||||||
\(989\) | 1.12600 | 0.0358048 | ||||||||
\(990\) | 2.44055 | 0.0775658 | ||||||||
\(991\) | − | 5.13468i | − | 0.163108i | −0.996669 | − | 0.0815542i | \(-0.974012\pi\) | ||
0.996669 | − | 0.0815542i | \(-0.0259884\pi\) | |||||||
\(992\) | 5.27795 | 0.167575 | ||||||||
\(993\) | − | 31.2779i | − | 0.992576i | ||||||
\(994\) | 42.9614i | 1.36265i | ||||||||
\(995\) | 20.4843 | 0.649395 | ||||||||
\(996\) | 7.71850 | 0.244570 | ||||||||
\(997\) | − | 12.1225i | − | 0.383922i | −0.981403 | − | 0.191961i | \(-0.938515\pi\) | ||
0.981403 | − | 0.191961i | \(-0.0614847\pi\) | |||||||
\(998\) | 36.7587 | 1.16357 | ||||||||
\(999\) | −0.198422 | − | 6.07953i | −0.00627780 | − | 0.192348i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1110.2.h.f.961.4 | yes | 6 | |
3.2 | odd | 2 | 3330.2.h.m.2071.1 | 6 | |||
37.36 | even | 2 | inner | 1110.2.h.f.961.1 | ✓ | 6 | |
111.110 | odd | 2 | 3330.2.h.m.2071.4 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1110.2.h.f.961.1 | ✓ | 6 | 37.36 | even | 2 | inner | |
1110.2.h.f.961.4 | yes | 6 | 1.1 | even | 1 | trivial | |
3330.2.h.m.2071.1 | 6 | 3.2 | odd | 2 | |||
3330.2.h.m.2071.4 | 6 | 111.110 | odd | 2 |