Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2100,2,Mod(1201,2100)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2100, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2100.1201");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2100.q (of order \(3\), 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: | \(16.7685844245\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 1201.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2100.1201 |
Dual form | 2100.2.q.e.1801.1 |
$q$-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 \(\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times\).
\(n\) | \(701\) | \(1051\) | \(1177\) | \(1501\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 | 0 | ||||||||
\(3\) | 0.500000 | − | 0.866025i | 0.288675 | − | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.00000 | + | 1.73205i | −0.755929 | + | 0.654654i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | + | 1.73205i | −0.301511 | + | 0.522233i | −0.976478 | − | 0.215615i | \(-0.930824\pi\) |
0.674967 | + | 0.737848i | \(0.264158\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.00000 | 0.554700 | 0.277350 | − | 0.960769i | \(-0.410544\pi\) | ||||
0.277350 | + | 0.960769i | \(0.410544\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.00000 | − | 1.73205i | 0.242536 | − | 0.420084i | −0.718900 | − | 0.695113i | \(-0.755354\pi\) |
0.961436 | + | 0.275029i | \(0.0886875\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.00000 | − | 3.46410i | −0.458831 | − | 0.794719i | 0.540068 | − | 0.841621i | \(-0.318398\pi\) |
−0.998899 | + | 0.0469020i | \(0.985065\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.500000 | + | 2.59808i | 0.109109 | + | 0.566947i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.00000 | − | 6.92820i | −0.834058 | − | 1.44463i | −0.894795 | − | 0.446476i | \(-0.852679\pi\) |
0.0607377 | − | 0.998154i | \(-0.480655\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.00000 | 0.742781 | 0.371391 | − | 0.928477i | \(-0.378881\pi\) | ||||
0.371391 | + | 0.928477i | \(0.378881\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.50000 | + | 2.59808i | −0.269408 | + | 0.466628i | −0.968709 | − | 0.248199i | \(-0.920161\pi\) |
0.699301 | + | 0.714827i | \(0.253495\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.00000 | + | 1.73205i | 0.174078 | + | 0.301511i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.50000 | − | 7.79423i | −0.739795 | − | 1.28136i | −0.952587 | − | 0.304266i | \(-0.901589\pi\) |
0.212792 | − | 0.977098i | \(-0.431744\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.00000 | − | 1.73205i | 0.160128 | − | 0.277350i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.00000 | 0.937043 | 0.468521 | − | 0.883452i | \(-0.344787\pi\) | ||||
0.468521 | + | 0.883452i | \(0.344787\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.00000 | 0.152499 | 0.0762493 | − | 0.997089i | \(-0.475706\pi\) | ||||
0.0762493 | + | 0.997089i | \(0.475706\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.00000 | − | 5.19615i | −0.437595 | − | 0.757937i | 0.559908 | − | 0.828554i | \(-0.310836\pi\) |
−0.997503 | + | 0.0706177i | \(0.977503\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | − | 6.92820i | 0.142857 | − | 0.989743i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.00000 | − | 1.73205i | −0.140028 | − | 0.242536i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.00000 | − | 1.73205i | 0.137361 | − | 0.237915i | −0.789136 | − | 0.614218i | \(-0.789471\pi\) |
0.926497 | + | 0.376303i | \(0.122805\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.00000 | −0.529813 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.00000 | − | 5.19615i | 0.390567 | − | 0.676481i | −0.601958 | − | 0.798528i | \(-0.705612\pi\) |
0.992524 | + | 0.122047i | \(0.0389457\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.500000 | + | 0.866025i | 0.0640184 | + | 0.110883i | 0.896258 | − | 0.443533i | \(-0.146275\pi\) |
−0.832240 | + | 0.554416i | \(0.812942\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.50000 | + | 0.866025i | 0.314970 | + | 0.109109i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.00000 | − | 10.3923i | 0.733017 | − | 1.26962i | −0.222571 | − | 0.974916i | \(-0.571445\pi\) |
0.955588 | − | 0.294706i | \(-0.0952216\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −8.00000 | −0.963087 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.0000 | 1.18678 | 0.593391 | − | 0.804914i | \(-0.297789\pi\) | ||||
0.593391 | + | 0.804914i | \(0.297789\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.500000 | − | 0.866025i | 0.0585206 | − | 0.101361i | −0.835281 | − | 0.549823i | \(-0.814695\pi\) |
0.893801 | + | 0.448463i | \(0.148028\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.00000 | − | 5.19615i | −0.113961 | − | 0.592157i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.50000 | − | 6.06218i | −0.393781 | − | 0.682048i | 0.599164 | − | 0.800626i | \(-0.295500\pi\) |
−0.992945 | + | 0.118578i | \(0.962166\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −18.0000 | −1.97576 | −0.987878 | − | 0.155230i | \(-0.950388\pi\) | ||||
−0.987878 | + | 0.155230i | \(0.950388\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.00000 | − | 3.46410i | 0.214423 | − | 0.371391i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.00000 | − | 8.66025i | −0.529999 | − | 0.917985i | −0.999388 | − | 0.0349934i | \(-0.988859\pi\) |
0.469389 | − | 0.882992i | \(-0.344474\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.00000 | + | 3.46410i | −0.419314 | + | 0.363137i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.50000 | + | 2.59808i | 0.155543 | + | 0.269408i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.00000 | −0.507673 | −0.253837 | − | 0.967247i | \(-0.581693\pi\) | ||||
−0.253837 | + | 0.967247i | \(0.581693\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.00000 | 0.201008 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.50000 | − | 9.52628i | −0.541931 | − | 0.938652i | −0.998793 | − | 0.0491146i | \(-0.984360\pi\) |
0.456862 | − | 0.889538i | \(-0.348973\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.00000 | + | 12.1244i | −0.670478 | + | 1.16130i | 0.307290 | + | 0.951616i | \(0.400578\pi\) |
−0.977769 | + | 0.209687i | \(0.932756\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −9.00000 | −0.854242 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.00000 | 0.564433 | 0.282216 | − | 0.959351i | \(-0.408930\pi\) | ||||
0.282216 | + | 0.959351i | \(0.408930\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.00000 | − | 1.73205i | −0.0924500 | − | 0.160128i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.00000 | + | 5.19615i | 0.0916698 | + | 0.476331i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.50000 | + | 6.06218i | 0.318182 | + | 0.551107i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.00000 | − | 5.19615i | 0.270501 | − | 0.468521i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −17.0000 | −1.50851 | −0.754253 | − | 0.656584i | \(-0.772001\pi\) | ||||
−0.754253 | + | 0.656584i | \(0.772001\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.500000 | − | 0.866025i | 0.0440225 | − | 0.0762493i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11.0000 | + | 19.0526i | 0.961074 | + | 1.66463i | 0.719811 | + | 0.694170i | \(0.244228\pi\) |
0.241264 | + | 0.970460i | \(0.422438\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 10.0000 | + | 3.46410i | 0.867110 | + | 0.300376i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.00000 | − | 13.8564i | 0.683486 | − | 1.18383i | −0.290424 | − | 0.956898i | \(-0.593796\pi\) |
0.973910 | − | 0.226935i | \(-0.0728704\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.00000 | 0.424094 | 0.212047 | − | 0.977259i | \(-0.431987\pi\) | ||||
0.212047 | + | 0.977259i | \(0.431987\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.00000 | −0.505291 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.00000 | + | 3.46410i | −0.167248 | + | 0.289683i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −5.50000 | − | 4.33013i | −0.453632 | − | 0.357143i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.00000 | − | 6.92820i | −0.327693 | − | 0.567581i | 0.654361 | − | 0.756182i | \(-0.272938\pi\) |
−0.982054 | + | 0.188602i | \(0.939604\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.50000 | + | 6.06218i | −0.284826 | + | 0.493333i | −0.972567 | − | 0.232623i | \(-0.925269\pi\) |
0.687741 | + | 0.725956i | \(0.258602\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.00000 | −0.161690 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.50000 | − | 2.59808i | 0.119713 | − | 0.207349i | −0.799941 | − | 0.600079i | \(-0.795136\pi\) |
0.919654 | + | 0.392730i | \(0.128469\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.00000 | − | 1.73205i | −0.0793052 | − | 0.137361i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 20.0000 | + | 6.92820i | 1.57622 | + | 0.546019i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.500000 | − | 0.866025i | −0.0391630 | − | 0.0678323i | 0.845780 | − | 0.533533i | \(-0.179136\pi\) |
−0.884943 | + | 0.465700i | \(0.845802\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 8.00000 | 0.619059 | 0.309529 | − | 0.950890i | \(-0.399829\pi\) | ||||
0.309529 | + | 0.950890i | \(0.399829\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.00000 | −0.692308 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.00000 | + | 3.46410i | −0.152944 | + | 0.264906i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.00000 | − | 5.19615i | −0.228086 | − | 0.395056i | 0.729155 | − | 0.684349i | \(-0.239913\pi\) |
−0.957241 | + | 0.289292i | \(0.906580\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.00000 | − | 5.19615i | −0.225494 | − | 0.390567i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −8.00000 | + | 13.8564i | −0.597948 | + | 1.03568i | 0.395175 | + | 0.918606i | \(0.370684\pi\) |
−0.993124 | + | 0.117071i | \(0.962650\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −15.0000 | −1.11494 | −0.557471 | − | 0.830197i | \(-0.688228\pi\) | ||||
−0.557471 | + | 0.830197i | \(0.688228\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.00000 | 0.0739221 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.00000 | + | 3.46410i | 0.146254 | + | 0.253320i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.00000 | − | 1.73205i | 0.145479 | − | 0.125988i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.00000 | + | 3.46410i | 0.144715 | + | 0.250654i | 0.929267 | − | 0.369410i | \(-0.120440\pi\) |
−0.784552 | + | 0.620063i | \(0.787107\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.500000 | + | 0.866025i | −0.0359908 | + | 0.0623379i | −0.883460 | − | 0.468507i | \(-0.844792\pi\) |
0.847469 | + | 0.530845i | \(0.178125\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 18.0000 | 1.28245 | 0.641223 | − | 0.767354i | \(-0.278427\pi\) | ||||
0.641223 | + | 0.767354i | \(0.278427\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.50000 | + | 2.59808i | −0.106332 | + | 0.184173i | −0.914282 | − | 0.405079i | \(-0.867244\pi\) |
0.807950 | + | 0.589252i | \(0.200577\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −6.00000 | − | 10.3923i | −0.423207 | − | 0.733017i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −8.00000 | + | 6.92820i | −0.561490 | + | 0.486265i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4.00000 | + | 6.92820i | −0.278019 | + | 0.481543i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8.00000 | 0.553372 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.00000 | −0.619586 | −0.309793 | − | 0.950804i | \(-0.600260\pi\) | ||||
−0.309793 | + | 0.950804i | \(0.600260\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 5.00000 | − | 8.66025i | 0.342594 | − | 0.593391i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.50000 | − | 7.79423i | −0.101827 | − | 0.529107i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.500000 | − | 0.866025i | −0.0337869 | − | 0.0585206i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.00000 | − | 3.46410i | 0.134535 | − | 0.233021i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −17.0000 | −1.13840 | −0.569202 | − | 0.822198i | \(-0.692748\pi\) | ||||
−0.569202 | + | 0.822198i | \(0.692748\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.00000 | + | 1.73205i | −0.0663723 | + | 0.114960i | −0.897302 | − | 0.441417i | \(-0.854476\pi\) |
0.830930 | + | 0.556378i | \(0.187809\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −13.0000 | − | 22.5167i | −0.859064 | − | 1.48794i | −0.872823 | − | 0.488037i | \(-0.837713\pi\) |
0.0137585 | − | 0.999905i | \(-0.495620\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −5.00000 | − | 1.73205i | −0.328976 | − | 0.113961i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2.00000 | − | 3.46410i | −0.131024 | − | 0.226941i | 0.793047 | − | 0.609160i | \(-0.208493\pi\) |
−0.924072 | + | 0.382219i | \(0.875160\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −7.00000 | −0.454699 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 18.0000 | 1.16432 | 0.582162 | − | 0.813073i | \(-0.302207\pi\) | ||||
0.582162 | + | 0.813073i | \(0.302207\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.50000 | − | 9.52628i | 0.354286 | − | 0.613642i | −0.632709 | − | 0.774389i | \(-0.718057\pi\) |
0.986996 | + | 0.160748i | \(0.0513906\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0.500000 | + | 0.866025i | 0.0320750 | + | 0.0555556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.00000 | − | 6.92820i | −0.254514 | − | 0.440831i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −9.00000 | + | 15.5885i | −0.570352 | + | 0.987878i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 16.0000 | 1.00591 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 11.0000 | + | 19.0526i | 0.686161 | + | 1.18847i | 0.973070 | + | 0.230508i | \(0.0740389\pi\) |
−0.286909 | + | 0.957958i | \(0.592628\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 22.5000 | + | 7.79423i | 1.39808 | + | 0.484310i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.00000 | − | 3.46410i | −0.123797 | − | 0.214423i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −11.0000 | + | 19.0526i | −0.678289 | + | 1.17483i | 0.297207 | + | 0.954813i | \(0.403945\pi\) |
−0.975496 | + | 0.220018i | \(0.929388\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −10.0000 | −0.611990 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6.00000 | − | 10.3923i | 0.365826 | − | 0.633630i | −0.623082 | − | 0.782157i | \(-0.714120\pi\) |
0.988908 | + | 0.148527i | \(0.0474530\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.00000 | − | 13.8564i | −0.485965 | − | 0.841717i | 0.513905 | − | 0.857847i | \(-0.328199\pi\) |
−0.999870 | + | 0.0161307i | \(0.994865\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.00000 | + | 5.19615i | 0.0605228 | + | 0.314485i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.00000 | + | 1.73205i | −0.0600842 | + | 0.104069i | −0.894503 | − | 0.447062i | \(-0.852470\pi\) |
0.834419 | + | 0.551131i | \(0.185804\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.00000 | 0.179605 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 30.0000 | 1.78965 | 0.894825 | − | 0.446417i | \(-0.147300\pi\) | ||||
0.894825 | + | 0.446417i | \(0.147300\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.00000 | − | 13.8564i | 0.475551 | − | 0.823678i | −0.524057 | − | 0.851683i | \(-0.675582\pi\) |
0.999608 | + | 0.0280052i | \(0.00891551\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −12.0000 | + | 10.3923i | −0.708338 | + | 0.613438i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.50000 | + | 11.2583i | 0.382353 | + | 0.662255i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.50000 | + | 4.33013i | −0.146553 | + | 0.253837i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6.00000 | 0.350524 | 0.175262 | − | 0.984522i | \(-0.443923\pi\) | ||||
0.175262 | + | 0.984522i | \(0.443923\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.00000 | − | 1.73205i | 0.0580259 | − | 0.100504i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −8.00000 | − | 13.8564i | −0.462652 | − | 0.801337i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.00000 | + | 1.73205i | −0.115278 | + | 0.0998337i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.00000 | 0.399511 | 0.199756 | − | 0.979846i | \(-0.435985\pi\) | ||||
0.199756 | + | 0.979846i | \(0.435985\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −11.0000 | −0.625768 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 16.0000 | − | 27.7128i | 0.907277 | − | 1.57145i | 0.0894452 | − | 0.995992i | \(-0.471491\pi\) |
0.817832 | − | 0.575458i | \(-0.195176\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 13.5000 | + | 23.3827i | 0.763065 | + | 1.32167i | 0.941263 | + | 0.337673i | \(0.109640\pi\) |
−0.178198 | + | 0.983995i | \(0.557027\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 17.0000 | + | 29.4449i | 0.954815 | + | 1.65379i | 0.734791 | + | 0.678294i | \(0.237280\pi\) |
0.220024 | + | 0.975494i | \(0.429386\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.00000 | + | 6.92820i | −0.223957 | + | 0.387905i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −8.00000 | −0.445132 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 7.00000 | + | 12.1244i | 0.387101 | + | 0.670478i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 15.0000 | + | 5.19615i | 0.826977 | + | 0.286473i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.5000 | − | 23.3827i | −0.742027 | − | 1.28523i | −0.951571 | − | 0.307429i | \(-0.900531\pi\) |
0.209544 | − | 0.977799i | \(-0.432802\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4.50000 | + | 7.79423i | −0.246598 | + | 0.427121i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.00000 | −0.490261 | −0.245131 | − | 0.969490i | \(-0.578831\pi\) | ||||
−0.245131 | + | 0.969490i | \(0.578831\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.00000 | − | 5.19615i | 0.162938 | − | 0.282216i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.00000 | − | 5.19615i | −0.162459 | − | 0.281387i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10.0000 | + | 15.5885i | 0.539949 | + | 0.841698i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 13.0000 | − | 22.5167i | 0.697877 | − | 1.20876i | −0.271325 | − | 0.962488i | \(-0.587462\pi\) |
0.969201 | − | 0.246270i | \(-0.0792049\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −34.0000 | −1.81998 | −0.909989 | − | 0.414632i | \(-0.863910\pi\) | ||||
−0.909989 | + | 0.414632i | \(0.863910\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.00000 | −0.106752 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 8.00000 | − | 13.8564i | 0.425797 | − | 0.737502i | −0.570697 | − | 0.821160i | \(-0.693327\pi\) |
0.996495 | + | 0.0836583i | \(0.0266604\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 5.00000 | + | 1.73205i | 0.264628 | + | 0.0916698i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 15.0000 | + | 25.9808i | 0.791670 | + | 1.37121i | 0.924932 | + | 0.380131i | \(0.124121\pi\) |
−0.133263 | + | 0.991081i | \(0.542545\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.50000 | − | 2.59808i | 0.0789474 | − | 0.136741i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 7.00000 | 0.367405 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −17.5000 | + | 30.3109i | −0.913493 | + | 1.58222i | −0.104399 | + | 0.994535i | \(0.533292\pi\) |
−0.809093 | + | 0.587680i | \(0.800041\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.00000 | − | 5.19615i | −0.156174 | − | 0.270501i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.00000 | + | 5.19615i | 0.0519174 | + | 0.269771i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.00000 | − | 8.66025i | −0.258890 | − | 0.448411i | 0.707055 | − | 0.707159i | \(-0.250023\pi\) |
−0.965945 | + | 0.258748i | \(0.916690\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 8.00000 | 0.412021 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 28.0000 | 1.43826 | 0.719132 | − | 0.694874i | \(-0.244540\pi\) | ||||
0.719132 | + | 0.694874i | \(0.244540\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −8.50000 | + | 14.7224i | −0.435468 | + | 0.754253i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −16.0000 | − | 27.7128i | −0.817562 | − | 1.41606i | −0.907474 | − | 0.420109i | \(-0.861992\pi\) |
0.0899119 | − | 0.995950i | \(-0.471341\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −0.500000 | − | 0.866025i | −0.0254164 | − | 0.0440225i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −5.00000 | + | 8.66025i | −0.253510 | + | 0.439092i | −0.964490 | − | 0.264120i | \(-0.914918\pi\) |
0.710980 | + | 0.703213i | \(0.248252\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −16.0000 | −0.809155 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 22.0000 | 1.10975 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 13.5000 | + | 23.3827i | 0.677546 | + | 1.17354i | 0.975718 | + | 0.219031i | \(0.0702897\pi\) |
−0.298172 | + | 0.954512i | \(0.596377\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 8.00000 | − | 6.92820i | 0.400501 | − | 0.346844i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.00000 | + | 1.73205i | 0.0499376 | + | 0.0864945i | 0.889914 | − | 0.456129i | \(-0.150764\pi\) |
−0.839976 | + | 0.542623i | \(0.817431\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.00000 | + | 5.19615i | −0.149441 | + | 0.258839i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 18.0000 | 0.892227 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7.00000 | − | 12.1244i | 0.346128 | − | 0.599511i | −0.639430 | − | 0.768849i | \(-0.720830\pi\) |
0.985558 | + | 0.169338i | \(0.0541630\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −8.00000 | − | 13.8564i | −0.394611 | − | 0.683486i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.00000 | + | 15.5885i | 0.147620 | + | 0.767058i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.50000 | − | 4.33013i | 0.122426 | − | 0.212047i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 8.00000 | 0.390826 | 0.195413 | − | 0.980721i | \(-0.437395\pi\) | ||||
0.195413 | + | 0.980721i | \(0.437395\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.0000 | 0.633581 | 0.316791 | − | 0.948495i | \(-0.397395\pi\) | ||||
0.316791 | + | 0.948495i | \(0.397395\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3.00000 | + | 5.19615i | −0.145865 | + | 0.252646i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.50000 | − | 0.866025i | −0.120983 | − | 0.0419099i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.00000 | + | 3.46410i | 0.0965609 | + | 0.167248i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.00000 | 0.240285 | 0.120142 | − | 0.992757i | \(-0.461665\pi\) | ||||
0.120142 | + | 0.992757i | \(0.461665\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −16.0000 | + | 27.7128i | −0.765384 | + | 1.32568i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.50000 | + | 9.52628i | 0.262501 | + | 0.454665i | 0.966906 | − | 0.255134i | \(-0.0821195\pi\) |
−0.704405 | + | 0.709798i | \(0.748786\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.50000 | + | 2.59808i | −0.309524 | + | 0.123718i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3.00000 | − | 5.19615i | −0.142534 | − | 0.246877i | 0.785916 | − | 0.618333i | \(-0.212192\pi\) |
−0.928450 | + | 0.371457i | \(0.878858\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −8.00000 | −0.378387 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 32.0000 | 1.51017 | 0.755087 | − | 0.655625i | \(-0.227595\pi\) | ||||
0.755087 | + | 0.655625i | \(0.227595\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.00000 | + | 10.3923i | −0.282529 | + | 0.489355i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3.50000 | + | 6.06218i | 0.164444 | + | 0.284826i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 18.5000 | + | 32.0429i | 0.865393 | + | 1.49891i | 0.866656 | + | 0.498906i | \(0.166265\pi\) |
−0.00126243 | + | 0.999999i | \(0.500402\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.00000 | + | 1.73205i | −0.0466760 | + | 0.0808452i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 14.0000 | 0.652045 | 0.326023 | − | 0.945362i | \(-0.394291\pi\) | ||||
0.326023 | + | 0.945362i | \(0.394291\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9.00000 | 0.418265 | 0.209133 | − | 0.977887i | \(-0.432936\pi\) | ||||
0.209133 | + | 0.977887i | \(0.432936\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3.00000 | + | 5.19615i | 0.138823 | + | 0.240449i | 0.927052 | − | 0.374934i | \(-0.122335\pi\) |
−0.788228 | + | 0.615383i | \(0.789001\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.00000 | + | 31.1769i | 0.277054 | + | 1.43962i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.50000 | − | 2.59808i | −0.0691164 | − | 0.119713i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.00000 | + | 1.73205i | −0.0459800 | + | 0.0796398i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.00000 | −0.0915737 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −16.0000 | + | 27.7128i | −0.731059 | + | 1.26623i | 0.225372 | + | 0.974273i | \(0.427640\pi\) |
−0.956431 | + | 0.291958i | \(0.905693\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9.00000 | − | 15.5885i | −0.410365 | − | 0.710772i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 16.0000 | − | 13.8564i | 0.728025 | − | 0.630488i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5.50000 | + | 9.52628i | −0.249229 | + | 0.431677i | −0.963312 | − | 0.268384i | \(-0.913510\pi\) |
0.714083 | + | 0.700061i | \(0.246844\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.00000 | −0.0452216 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −36.0000 | −1.62466 | −0.812329 | − | 0.583200i | \(-0.801800\pi\) | ||||
−0.812329 | + | 0.583200i | \(0.801800\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.00000 | − | 6.92820i | 0.180151 | − | 0.312031i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −20.0000 | + | 17.3205i | −0.897123 | + | 0.776931i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −18.0000 | − | 31.1769i | −0.805791 | − | 1.39567i | −0.915756 | − | 0.401735i | \(-0.868407\pi\) |
0.109965 | − | 0.993935i | \(-0.464926\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4.00000 | − | 6.92820i | 0.178707 | − | 0.309529i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −40.0000 | −1.78351 | −0.891756 | − | 0.452517i | \(-0.850526\pi\) | ||||
−0.891756 | + | 0.452517i | \(0.850526\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −4.50000 | + | 7.79423i | −0.199852 | + | 0.346154i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −9.00000 | − | 15.5885i | −0.398918 | − | 0.690946i | 0.594675 | − | 0.803966i | \(-0.297281\pi\) |
−0.993593 | + | 0.113020i | \(0.963948\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.500000 | + | 2.59808i | 0.0221187 | + | 0.114932i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.00000 | + | 3.46410i | 0.0883022 | + | 0.152944i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 12.0000 | 0.527759 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −6.00000 | −0.263371 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.00000 | − | 5.19615i | 0.131432 | − | 0.227648i | −0.792797 | − | 0.609486i | \(-0.791376\pi\) |
0.924229 | + | 0.381839i | \(0.124709\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.500000 | + | 0.866025i | 0.0218635 | + | 0.0378686i | 0.876750 | − | 0.480946i | \(-0.159707\pi\) |
−0.854887 | + | 0.518815i | \(0.826373\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.00000 | + | 5.19615i | 0.130682 | + | 0.226348i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.5000 | + | 35.5070i | −0.891304 | + | 1.54378i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6.00000 | −0.260378 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 12.0000 | 0.519778 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 8.00000 | + | 13.8564i | 0.345225 | + | 0.597948i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 11.0000 | + | 8.66025i | 0.473804 | + | 0.373024i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.00000 | + | 8.66025i | 0.214967 | + | 0.372333i | 0.953262 | − | 0.302144i | \(-0.0977023\pi\) |
−0.738296 | + | 0.674477i | \(0.764369\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −7.50000 | + | 12.9904i | −0.321856 | + | 0.557471i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12.0000 | −0.513083 | −0.256541 | − | 0.966533i | \(-0.582583\pi\) | ||||
−0.256541 | + | 0.966533i | \(0.582583\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.500000 | − | 0.866025i | 0.0213395 | − | 0.0369611i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −8.00000 | − | 13.8564i | −0.340811 | − | 0.590303i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 17.5000 | + | 6.06218i | 0.744176 | + | 0.257790i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 9.00000 | − | 15.5885i | 0.381342 | − | 0.660504i | −0.609912 | − | 0.792469i | \(-0.708795\pi\) |
0.991254 | + | 0.131965i | \(0.0421286\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.00000 | 0.0845910 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.00000 | 0.168880 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −17.0000 | + | 29.4449i | −0.716465 | + | 1.24095i | 0.245927 | + | 0.969288i | \(0.420908\pi\) |
−0.962392 | + | 0.271665i | \(0.912426\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.500000 | − | 2.59808i | −0.0209980 | − | 0.109109i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 2.00000 | + | 3.46410i | 0.0838444 | + | 0.145223i | 0.904898 | − | 0.425628i | \(-0.139947\pi\) |
−0.821054 | + | 0.570851i | \(0.806613\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.00000 | + | 3.46410i | −0.0836974 | + | 0.144968i | −0.904835 | − | 0.425762i | \(-0.860006\pi\) |
0.821138 | + | 0.570730i | \(0.193340\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4.00000 | 0.167102 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 15.5000 | − | 26.8468i | 0.645273 | − | 1.11765i | −0.338965 | − | 0.940799i | \(-0.610077\pi\) |
0.984238 | − | 0.176847i | \(-0.0565899\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0.500000 | + | 0.866025i | 0.0207793 | + | 0.0359908i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 36.0000 | − | 31.1769i | 1.49353 | − | 1.29344i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.00000 | + | 3.46410i | 0.0828315 | + | 0.143468i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 42.0000 | 1.73353 | 0.866763 | − | 0.498721i | \(-0.166197\pi\) | ||||
0.866763 | + | 0.498721i | \(0.166197\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 12.0000 | 0.494451 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 9.00000 | − | 15.5885i | 0.370211 | − | 0.641223i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −12.0000 | − | 20.7846i | −0.492781 | − | 0.853522i | 0.507184 | − | 0.861838i | \(-0.330686\pi\) |
−0.999965 | + | 0.00831589i | \(0.997353\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.50000 | + | 2.59808i | 0.0613909 | + | 0.106332i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −24.0000 | + | 41.5692i | −0.980613 | + | 1.69847i | −0.320607 | + | 0.947212i | \(0.603887\pi\) |
−0.660006 | + | 0.751260i | \(0.729446\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −26.0000 | −1.06056 | −0.530281 | − | 0.847822i | \(-0.677914\pi\) | ||||
−0.530281 | + | 0.847822i | \(0.677914\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −12.0000 | −0.488678 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 21.5000 | + | 37.2391i | 0.872658 | + | 1.51149i | 0.859237 | + | 0.511578i | \(0.170939\pi\) |
0.0134214 | + | 0.999910i | \(0.495728\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.00000 | + | 10.3923i | 0.0810441 | + | 0.421117i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6.00000 | − | 10.3923i | −0.242734 | − | 0.420428i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −15.0000 | + | 25.9808i | −0.605844 | + | 1.04935i | 0.386073 | + | 0.922468i | \(0.373831\pi\) |
−0.991917 | + | 0.126885i | \(0.959502\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −14.0000 | −0.563619 | −0.281809 | − | 0.959470i | \(-0.590935\pi\) | ||||
−0.281809 | + | 0.959470i | \(0.590935\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 15.5000 | − | 26.8468i | 0.622998 | − | 1.07906i | −0.365927 | − | 0.930644i | \(-0.619248\pi\) |
0.988924 | − | 0.148420i | \(-0.0474187\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.00000 | + | 6.92820i | 0.160514 | + | 0.278019i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 25.0000 | + | 8.66025i | 1.00160 | + | 0.346966i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.00000 | − | 6.92820i | 0.159745 | − | 0.276686i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −18.0000 | −0.717707 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 29.0000 | 1.15447 | 0.577236 | − | 0.816577i | \(-0.304131\pi\) | ||||
0.577236 | + | 0.816577i | \(0.304131\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −4.50000 | + | 7.79423i | −0.178859 | + | 0.309793i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.00000 | − | 13.8564i | 0.0792429 | − | 0.549011i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −5.00000 | − | 8.66025i | −0.197797 | − | 0.342594i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5.00000 | + | 8.66025i | −0.197488 | + | 0.342059i | −0.947713 | − | 0.319123i | \(-0.896612\pi\) |
0.750225 | + | 0.661182i | \(0.229945\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5.00000 | −0.197181 | −0.0985904 | − | 0.995128i | \(-0.531433\pi\) | ||||
−0.0985904 | + | 0.995128i | \(0.531433\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −3.00000 | + | 5.19615i | −0.117942 | + | 0.204282i | −0.918952 | − | 0.394369i | \(-0.870963\pi\) |
0.801010 | + | 0.598651i | \(0.204296\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.00000 | + | 10.3923i | 0.235521 | + | 0.407934i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −7.50000 | − | 2.59808i | −0.293948 | − | 0.101827i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 13.0000 | + | 22.5167i | 0.508729 | + | 0.881145i | 0.999949 | + | 0.0101092i | \(0.00321793\pi\) |
−0.491220 | + | 0.871036i | \(0.663449\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.00000 | −0.0390137 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 42.0000 | 1.63609 | 0.818044 | − | 0.575156i | \(-0.195059\pi\) | ||||
0.818044 | + | 0.575156i | \(0.195059\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.50000 | + | 9.52628i | −0.213925 | + | 0.370529i | −0.952940 | − | 0.303160i | \(-0.901958\pi\) |
0.739014 | + | 0.673690i | \(0.235292\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.00000 | − | 3.46410i | −0.0776736 | − | 0.134535i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −16.0000 | − | 27.7128i | −0.619522 | − | 1.07304i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −8.50000 | + | 14.7224i | −0.328629 | + | 0.569202i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.00000 | −0.0772091 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.00000 | 0.346925 | 0.173462 | − | 0.984841i | \(-0.444505\pi\) | ||||
0.173462 | + | 0.984841i | \(0.444505\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −16.0000 | − | 27.7128i | −0.614930 | − | 1.06509i | −0.990397 | − | 0.138254i | \(-0.955851\pi\) |
0.375467 | − | 0.926836i | \(-0.377482\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 10.0000 | − | 8.66025i | 0.383765 | − | 0.332350i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.00000 | + | 1.73205i | 0.0383201 | + | 0.0663723i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −3.00000 | + | 5.19615i | −0.114792 | + | 0.198825i | −0.917697 | − | 0.397282i | \(-0.869953\pi\) |
0.802905 | + | 0.596107i | \(0.203287\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −26.0000 | −0.991962 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.00000 | − | 3.46410i | 0.0761939 | − | 0.131972i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −13.5000 | − | 23.3827i | −0.513564 | − | 0.889519i | −0.999876 | − | 0.0157341i | \(-0.994991\pi\) |
0.486312 | − | 0.873785i | \(-0.338342\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −4.00000 | + | 3.46410i | −0.151947 | + | 0.131590i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.00000 | − | 10.3923i | 0.227266 | − | 0.393637i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −4.00000 | −0.151294 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −18.0000 | −0.679851 | −0.339925 | − | 0.940452i | \(-0.610402\pi\) | ||||
−0.339925 | + | 0.940452i | \(0.610402\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −18.0000 | + | 31.1769i | −0.678883 | + | 1.17586i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.50000 | + | 9.52628i | 0.206557 | + | 0.357767i | 0.950628 | − | 0.310334i | \(-0.100441\pi\) |
−0.744071 | + | 0.668101i | \(0.767108\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.50000 | + | 6.06218i | −0.131260 | + | 0.227349i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 24.0000 | 0.898807 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 9.00000 | − | 15.5885i | 0.336111 | − | 0.582162i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −22.0000 | − | 38.1051i | −0.820462 | − | 1.42108i | −0.905339 | − | 0.424690i | \(-0.860383\pi\) |
0.0848774 | − | 0.996391i | \(-0.472950\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 27.5000 | + | 9.52628i | 1.02415 | + | 0.354777i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −5.50000 | − | 9.52628i | −0.204547 | − | 0.354286i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −8.00000 | −0.296704 | −0.148352 | − | 0.988935i | \(-0.547397\pi\) | ||||
−0.148352 | + | 0.988935i | \(0.547397\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.00000 | − | 1.73205i | 0.0369863 | − | 0.0640622i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −17.5000 | − | 30.3109i | −0.646377 | − | 1.11956i | −0.983982 | − | 0.178270i | \(-0.942950\pi\) |
0.337604 | − | 0.941288i | \(-0.390383\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 12.0000 | + | 20.7846i | 0.442026 | + | 0.765611i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −20.5000 | + | 35.5070i | −0.754105 | + | 1.30615i | 0.191714 | + | 0.981451i | \(0.438596\pi\) |
−0.945818 | + | 0.324697i | \(0.894738\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −8.00000 | −0.293887 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 12.0000 | 0.440237 | 0.220119 | − | 0.975473i | \(-0.429356\pi\) | ||||
0.220119 | + | 0.975473i | \(0.429356\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 9.00000 | + | 15.5885i | 0.329293 | + | 0.570352i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12.5000 | − | 21.6506i | −0.456131 | − | 0.790043i | 0.542621 | − | 0.839978i | \(-0.317432\pi\) |
−0.998752 | + | 0.0499348i | \(0.984099\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −13.0000 | −0.472493 | −0.236247 | − | 0.971693i | \(-0.575917\pi\) | ||||
−0.236247 | + | 0.971693i | \(0.575917\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 8.00000 | − | 13.8564i | 0.290382 | − | 0.502956i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 16.0000 | + | 27.7128i | 0.580000 | + | 1.00459i | 0.995479 | + | 0.0949859i | \(0.0302806\pi\) |
−0.415479 | + | 0.909603i | \(0.636386\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7.00000 | − | 36.3731i | −0.253417 | − | 1.31679i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 6.00000 | − | 10.3923i | 0.216647 | − | 0.375244i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −29.0000 | −1.04577 | −0.522883 | − | 0.852404i | \(-0.675144\pi\) | ||||
−0.522883 | + | 0.852404i | \(0.675144\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 22.0000 | 0.792311 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 14.0000 | − | 24.2487i | 0.503545 | − | 0.872166i | −0.496447 | − | 0.868067i | \(-0.665362\pi\) |
0.999992 | − | 0.00409826i | \(-0.00130452\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 18.0000 | − | 15.5885i | 0.645746 | − | 0.559233i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −12.0000 | − | 20.7846i | −0.429945 | − | 0.744686i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −10.0000 | + | 17.3205i | −0.357828 | + | 0.619777i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4.00000 | −0.142948 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5.50000 | − | 9.52628i | 0.196054 | − | 0.339575i | −0.751192 | − | 0.660084i | \(-0.770521\pi\) |
0.947245 | + | 0.320509i | \(0.103854\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 11.0000 | + | 19.0526i | 0.391610 | + | 0.678289i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −12.0000 | + | 10.3923i | −0.426671 | + | 0.369508i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.00000 | + | 1.73205i | 0.0355110 | + | 0.0615069i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 12.0000 | 0.425062 | 0.212531 | − | 0.977154i | \(-0.431829\pi\) | ||||
0.212531 | + | 0.977154i | \(0.431829\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −12.0000 | −0.424529 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −5.00000 | + | 8.66025i | −0.176666 | + | 0.305995i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.00000 | + | 1.73205i | 0.0352892 | + | 0.0611227i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −6.00000 | − | 10.3923i | −0.211210 | − | 0.365826i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 14.0000 | − | 24.2487i | 0.492214 | − | 0.852539i | −0.507746 | − | 0.861507i | \(-0.669521\pi\) |
0.999960 | + | 0.00896753i | \(0.00285449\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 43.0000 | 1.50993 | 0.754967 | − | 0.655763i | \(-0.227653\pi\) | ||||
0.754967 | + | 0.655763i | \(0.227653\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −16.0000 | −0.561144 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.00000 | − | 3.46410i | −0.0699711 | − | 0.121194i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 5.00000 | + | 1.73205i | 0.174714 | + | 0.0605228i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 4.00000 | + | 6.92820i | 0.139601 | + | 0.241796i | 0.927346 | − | 0.374206i | \(-0.122085\pi\) |
−0.787745 | + | 0.616002i | \(0.788751\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −7.50000 | + | 12.9904i | −0.261434 | + | 0.452816i | −0.966623 | − | 0.256203i | \(-0.917529\pi\) |
0.705190 | + | 0.709019i | \(0.250862\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 14.0000 | 0.486828 | 0.243414 | − | 0.969923i | \(-0.421733\pi\) | ||||
0.243414 | + | 0.969923i | \(0.421733\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −4.50000 | + | 7.79423i | −0.156291 | + | 0.270705i | −0.933529 | − | 0.358503i | \(-0.883287\pi\) |
0.777237 | + | 0.629208i | \(0.216621\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.00000 | + | 1.73205i | 0.0346896 | + | 0.0600842i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −11.0000 | − | 8.66025i | −0.381127 | − | 0.300060i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.50000 | − | 2.59808i | 0.0518476 | − | 0.0898027i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −34.0000 | −1.17381 | −0.586905 | − | 0.809656i | \(-0.699654\pi\) | ||||
−0.586905 | + | 0.809656i | \(0.699654\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13.0000 | −0.448276 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 15.0000 | − | 25.9808i | 0.516627 | − | 0.894825i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −17.5000 | − | 6.06218i | −0.601307 | − | 0.208299i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −8.00000 | − | 13.8564i | −0.274559 | − | 0.475551i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −36.0000 | + | 62.3538i | −1.23406 | + | 2.13746i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −7.00000 | −0.239675 | −0.119838 | − | 0.992793i | \(-0.538237\pi\) | ||||
−0.119838 | + | 0.992793i | \(0.538237\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −20.0000 | + | 34.6410i | −0.683187 | + | 1.18331i | 0.290816 | + | 0.956779i | \(0.406073\pi\) |
−0.974003 | + | 0.226536i | \(0.927260\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −14.0000 | − | 24.2487i | −0.477674 | − | 0.827355i | 0.521999 | − | 0.852946i | \(-0.325187\pi\) |
−0.999672 | + | 0.0255910i | \(0.991853\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.00000 | + | 15.5885i | 0.102240 | + | 0.531253i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 7.00000 | + | 12.1244i | 0.238283 | + | 0.412718i | 0.960222 | − | 0.279239i | \(-0.0900822\pi\) |
−0.721939 | + | 0.691957i | \(0.756749\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 13.0000 | 0.441503 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 14.0000 | 0.474917 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 12.0000 | − | 20.7846i | 0.406604 | − | 0.704260i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.50000 | + | 4.33013i | 0.0846122 | + | 0.146553i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 11.5000 | + | 19.9186i | 0.388327 | + | 0.672603i | 0.992225 | − | 0.124459i | \(-0.0397196\pi\) |
−0.603897 | + | 0.797062i | \(0.706386\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 3.00000 | − | 5.19615i | 0.101187 | − | 0.175262i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −22.0000 | −0.741199 | −0.370599 | − | 0.928793i | \(-0.620848\pi\) | ||||
−0.370599 | + | 0.928793i | \(0.620848\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4.00000 | 0.134611 | 0.0673054 | − | 0.997732i | \(-0.478560\pi\) | ||||
0.0673054 | + | 0.997732i | \(0.478560\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −17.0000 | − | 29.4449i | −0.570804 | − | 0.988662i | −0.996484 | − | 0.0837878i | \(-0.973298\pi\) |
0.425679 | − | 0.904874i | \(-0.360035\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 34.0000 | − | 29.4449i | 1.14032 | − | 0.987549i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.00000 | − | 1.73205i | −0.0335013 | − | 0.0580259i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −12.0000 | + | 20.7846i | −0.401565 | + | 0.695530i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −16.0000 | −0.534224 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −6.00000 | + | 10.3923i | −0.200111 | + | 0.346603i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.00000 | − | 3.46410i | −0.0666297 | − | 0.115406i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.500000 | + | 2.59808i | 0.0166390 | + | 0.0864586i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 9.50000 | − | 16.4545i | 0.315442 | − | 0.546362i | −0.664089 | − | 0.747653i | \(-0.731180\pi\) |
0.979531 | + | 0.201291i | \(0.0645138\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 8.00000 | 0.265052 | 0.132526 | − | 0.991180i | \(-0.457691\pi\) | ||||
0.132526 | + | 0.991180i | \(0.457691\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 18.0000 | − | 31.1769i | 0.595713 | − | 1.03181i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −55.0000 | − | 19.0526i | −1.81626 | − | 0.629171i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5.50000 | + | 9.52628i | 0.181428 | + | 0.314243i | 0.942367 | − | 0.334581i | \(-0.108595\pi\) |
−0.760939 | + | 0.648824i | \(0.775261\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3.50000 | − | 6.06218i | 0.115329 | − | 0.199756i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 20.0000 | 0.658308 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −5.50000 | + | 9.52628i | −0.180644 | + | 0.312884i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −23.0000 | − | 39.8372i | −0.754606 | − | 1.30702i | −0.945570 | − | 0.325418i | \(-0.894495\pi\) |
0.190965 | − | 0.981597i | \(-0.438838\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −26.0000 | + | 10.3923i | −0.852116 | + | 0.340594i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −16.0000 | − | 27.7128i | −0.523816 | − | 0.907277i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −19.0000 | −0.620703 | −0.310351 | − | 0.950622i | \(-0.600447\pi\) | ||||
−0.310351 | + | 0.950622i | \(0.600447\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 27.0000 | 0.881112 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 9.00000 | − | 15.5885i | 0.293392 | − | 0.508169i | −0.681218 | − | 0.732081i | \(-0.738549\pi\) |
0.974609 | + | 0.223912i | \(0.0718827\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −24.0000 | − | 41.5692i | −0.781548 | − | 1.35368i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −25.0000 | − | 43.3013i | −0.812391 | − | 1.40710i | −0.911186 | − | 0.411994i | \(-0.864832\pi\) |
0.0987955 | − | 0.995108i | \(-0.468501\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.00000 | − | 1.73205i | 0.0324614 | − | 0.0562247i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 34.0000 | 1.10253 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 52.0000 | 1.68445 | 0.842223 | − | 0.539130i | \(-0.181247\pi\) | ||||
0.842223 | + | 0.539130i | \(0.181247\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 4.00000 | + | 6.92820i | 0.129302 | + | 0.223957i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 8.00000 | + | 41.5692i | 0.258333 | + | 1.34234i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 11.0000 | + | 19.0526i | 0.354839 | + | 0.614599i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −31.0000 | −0.996893 | −0.498446 | − | 0.866921i | \(-0.666096\pi\) | ||||
−0.498446 | + | 0.866921i | \(0.666096\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −4.00000 | + | 6.92820i | −0.128499 | + | 0.222566i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 22.0000 | + | 38.1051i | 0.706014 | + | 1.22285i | 0.966324 | + | 0.257327i | \(0.0828416\pi\) |
−0.260311 | + | 0.965525i | \(0.583825\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −10.0000 | + | 8.66025i | −0.320585 | + | 0.277635i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −6.00000 | + | 10.3923i | −0.191957 | + | 0.332479i | −0.945899 | − | 0.324462i | \(-0.894817\pi\) |
0.753942 | + | 0.656941i | \(0.228150\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 20.0000 | 0.639203 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 14.0000 | 0.446986 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −9.00000 | + | 15.5885i | −0.287055 | + | 0.497195i | −0.973106 | − | 0.230360i | \(-0.926010\pi\) |
0.686050 | + | 0.727554i | \(0.259343\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 12.0000 | − | 10.3923i | 0.381964 | − | 0.330791i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.00000 | − | 6.92820i | −0.127193 | − | 0.220304i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −15.5000 | + | 26.8468i | −0.492374 | + | 0.852816i | −0.999961 | − | 0.00878379i | \(-0.997204\pi\) |
0.507588 | + | 0.861600i | \(0.330537\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −27.0000 | −0.856819 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 15.5000 | − | 26.8468i | 0.490890 | − | 0.850246i | −0.509055 | − | 0.860734i | \(-0.670005\pi\) |
0.999945 | + | 0.0104877i | \(0.00333839\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4.50000 | + | 7.79423i | 0.142374 | + | 0.246598i |
(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 | 2100.2.q.e.1201.1 | yes | 2 | |
5.2 | odd | 4 | 2100.2.bc.b.949.1 | 4 | |||
5.3 | odd | 4 | 2100.2.bc.b.949.2 | 4 | |||
5.4 | even | 2 | 2100.2.q.c.1201.1 | ✓ | 2 | ||
7.2 | even | 3 | inner | 2100.2.q.e.1801.1 | yes | 2 | |
35.2 | odd | 12 | 2100.2.bc.b.1549.2 | 4 | |||
35.9 | even | 6 | 2100.2.q.c.1801.1 | yes | 2 | ||
35.23 | odd | 12 | 2100.2.bc.b.1549.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2100.2.q.c.1201.1 | ✓ | 2 | 5.4 | even | 2 | ||
2100.2.q.c.1801.1 | yes | 2 | 35.9 | even | 6 | ||
2100.2.q.e.1201.1 | yes | 2 | 1.1 | even | 1 | trivial | |
2100.2.q.e.1801.1 | yes | 2 | 7.2 | even | 3 | inner | |
2100.2.bc.b.949.1 | 4 | 5.2 | odd | 4 | |||
2100.2.bc.b.949.2 | 4 | 5.3 | odd | 4 | |||
2100.2.bc.b.1549.1 | 4 | 35.23 | odd | 12 | |||
2100.2.bc.b.1549.2 | 4 | 35.2 | odd | 12 |