Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2100,2,Mod(949,2100)]
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, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2100.949");
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.bc (of order \(6\), degree \(2\), not 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: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1549.1 | ||
Root | \(0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2100.1549 |
Dual form | 2100.2.bc.b.949.1 |
$q$-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 \(\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times\).
\(n\) | \(701\) | \(1051\) | \(1177\) | \(1501\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) |
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 | ||||||||
\(3\) | −0.866025 | + | 0.500000i | −0.500000 | + | 0.288675i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.73205 | + | 2.00000i | −0.654654 | + | 0.755929i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.500000 | − | 0.866025i | 0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | − | 1.73205i | −0.301511 | − | 0.522233i | 0.674967 | − | 0.737848i | \(-0.264158\pi\) |
−0.976478 | + | 0.215615i | \(0.930824\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.00000i | 0.554700i | 0.960769 | + | 0.277350i | \(0.0894562\pi\) | ||||
−0.960769 | + | 0.277350i | \(0.910544\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.73205 | − | 1.00000i | 0.420084 | − | 0.242536i | −0.275029 | − | 0.961436i | \(-0.588688\pi\) |
0.695113 | + | 0.718900i | \(0.255354\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.00000 | − | 3.46410i | 0.458831 | − | 0.794719i | −0.540068 | − | 0.841621i | \(-0.681602\pi\) |
0.998899 | + | 0.0469020i | \(0.0149348\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.500000 | − | 2.59808i | 0.109109 | − | 0.566947i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.92820 | − | 4.00000i | −1.44463 | − | 0.834058i | −0.446476 | − | 0.894795i | \(-0.647321\pi\) |
−0.998154 | + | 0.0607377i | \(0.980655\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.00000 | −0.742781 | −0.371391 | − | 0.928477i | \(-0.621119\pi\) | ||||
−0.371391 | + | 0.928477i | \(0.621119\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.50000 | − | 2.59808i | −0.269408 | − | 0.466628i | 0.699301 | − | 0.714827i | \(-0.253495\pi\) |
−0.968709 | + | 0.248199i | \(0.920161\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.73205 | + | 1.00000i | 0.301511 | + | 0.174078i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.79423 | + | 4.50000i | 1.28136 | + | 0.739795i | 0.977098 | − | 0.212792i | \(-0.0682556\pi\) |
0.304266 | + | 0.952587i | \(0.401589\pi\) | |||||||
\(38\) | 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 | ||||||||
\(43\) | 1.00000i | 0.152499i | 0.997089 | + | 0.0762493i | \(0.0242945\pi\) | ||||
−0.997089 | + | 0.0762493i | \(0.975706\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.19615 | + | 3.00000i | 0.757937 | + | 0.437595i | 0.828554 | − | 0.559908i | \(-0.189164\pi\) |
−0.0706177 | + | 0.997503i | \(0.522497\pi\) | |||||||
\(48\) | 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 | ||||||||
\(53\) | −1.73205 | + | 1.00000i | −0.237915 | + | 0.137361i | −0.614218 | − | 0.789136i | \(-0.710529\pi\) |
0.376303 | + | 0.926497i | \(0.377195\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.00000i | 0.529813i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.00000 | − | 5.19615i | −0.390567 | − | 0.676481i | 0.601958 | − | 0.798528i | \(-0.294388\pi\) |
−0.992524 | + | 0.122047i | \(0.961054\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.500000 | − | 0.866025i | 0.0640184 | − | 0.110883i | −0.832240 | − | 0.554416i | \(-0.812942\pi\) |
0.896258 | + | 0.443533i | \(0.146275\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.866025 | + | 2.50000i | 0.109109 | + | 0.314970i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.3923 | − | 6.00000i | 1.26962 | − | 0.733017i | 0.294706 | − | 0.955588i | \(-0.404778\pi\) |
0.974916 | + | 0.222571i | \(0.0714450\pi\) | |||||||
\(68\) | 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 | ||||||||
\(73\) | −0.866025 | + | 0.500000i | −0.101361 | + | 0.0585206i | −0.549823 | − | 0.835281i | \(-0.685305\pi\) |
0.448463 | + | 0.893801i | \(0.351972\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.19615 | + | 1.00000i | 0.592157 | + | 0.113961i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.50000 | − | 6.06218i | 0.393781 | − | 0.682048i | −0.599164 | − | 0.800626i | \(-0.704500\pi\) |
0.992945 | + | 0.118578i | \(0.0378336\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 18.0000i | − | 1.97576i | −0.155230 | − | 0.987878i | \(-0.549612\pi\) | ||
0.155230 | − | 0.987878i | \(-0.450388\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.46410 | − | 2.00000i | 0.371391 | − | 0.214423i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.00000 | − | 8.66025i | 0.529999 | − | 0.917985i | −0.469389 | − | 0.882992i | \(-0.655526\pi\) |
0.999388 | − | 0.0349934i | \(-0.0111410\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.00000 | − | 3.46410i | −0.419314 | − | 0.363137i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.59808 | + | 1.50000i | 0.269408 | + | 0.155543i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.00000i | 0.507673i | 0.967247 | + | 0.253837i | \(0.0816925\pi\) | ||||
−0.967247 | + | 0.253837i | \(0.918307\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.00000 | −0.201008 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.52628 | − | 5.50000i | −0.938652 | − | 0.541931i | −0.0491146 | − | 0.998793i | \(-0.515640\pi\) |
−0.889538 | + | 0.456862i | \(0.848973\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.00000 | + | 12.1244i | 0.670478 | + | 1.16130i | 0.977769 | + | 0.209687i | \(0.0672444\pi\) |
−0.307290 | + | 0.951616i | \(0.599422\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −9.00000 | −0.854242 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.00000i | 0.564433i | 0.959351 | + | 0.282216i | \(0.0910696\pi\) | ||||
−0.959351 | + | 0.282216i | \(0.908930\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.73205 | + | 1.00000i | 0.160128 | + | 0.0924500i | ||||
\(118\) | 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 | ||||||||
\(123\) | −5.19615 | + | 3.00000i | −0.468521 | + | 0.270501i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 17.0000i | 1.50851i | 0.656584 | + | 0.754253i | \(0.272001\pi\) | ||||
−0.656584 | + | 0.754253i | \(0.727999\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.500000 | − | 0.866025i | −0.0440225 | − | 0.0762493i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11.0000 | − | 19.0526i | 0.961074 | − | 1.66463i | 0.241264 | − | 0.970460i | \(-0.422438\pi\) |
0.719811 | − | 0.694170i | \(-0.244228\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.46410 | + | 10.0000i | 0.300376 | + | 0.867110i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 13.8564 | − | 8.00000i | 1.18383 | − | 0.683486i | 0.226935 | − | 0.973910i | \(-0.427130\pi\) |
0.956898 | + | 0.290424i | \(0.0937963\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.00000 | −0.424094 | −0.212047 | − | 0.977259i | \(-0.568013\pi\) | ||||
−0.212047 | + | 0.977259i | \(0.568013\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.00000 | −0.505291 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.46410 | − | 2.00000i | 0.289683 | − | 0.167248i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 4.33013 | + | 5.50000i | 0.357143 | + | 0.453632i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.00000 | − | 6.92820i | 0.327693 | − | 0.567581i | −0.654361 | − | 0.756182i | \(-0.727062\pi\) |
0.982054 | + | 0.188602i | \(0.0603956\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.50000 | − | 6.06218i | −0.284826 | − | 0.493333i | 0.687741 | − | 0.725956i | \(-0.258602\pi\) |
−0.972567 | + | 0.232623i | \(0.925269\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 2.00000i | − | 0.161690i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.59808 | − | 1.50000i | 0.207349 | − | 0.119713i | −0.392730 | − | 0.919654i | \(-0.628469\pi\) |
0.600079 | + | 0.799941i | \(0.295136\pi\) | |||||||
\(158\) | 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 | ||||||||
\(163\) | −0.866025 | − | 0.500000i | −0.0678323 | − | 0.0391630i | 0.465700 | − | 0.884943i | \(-0.345802\pi\) |
−0.533533 | + | 0.845780i | \(0.679136\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 8.00000i | − | 0.619059i | −0.950890 | − | 0.309529i | \(-0.899829\pi\) | ||
0.950890 | − | 0.309529i | \(-0.100171\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.00000 | 0.692308 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.00000 | − | 3.46410i | −0.152944 | − | 0.264906i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −5.19615 | − | 3.00000i | −0.395056 | − | 0.228086i | 0.289292 | − | 0.957241i | \(-0.406580\pi\) |
−0.684349 | + | 0.729155i | \(0.739913\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5.19615 | + | 3.00000i | 0.390567 | + | 0.225494i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.00000 | + | 13.8564i | 0.597948 | + | 1.03568i | 0.993124 | + | 0.117071i | \(0.0373504\pi\) |
−0.395175 | + | 0.918606i | \(0.629316\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −15.0000 | −1.11494 | −0.557471 | − | 0.830197i | \(-0.688228\pi\) | ||||
−0.557471 | + | 0.830197i | \(0.688228\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.00000i | 0.0739221i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.46410 | − | 2.00000i | −0.253320 | − | 0.146254i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.00000 | − | 1.73205i | −0.145479 | − | 0.125988i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.00000 | − | 3.46410i | 0.144715 | − | 0.250654i | −0.784552 | − | 0.620063i | \(-0.787107\pi\) |
0.929267 | + | 0.369410i | \(0.120440\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.866025 | − | 0.500000i | 0.0623379 | − | 0.0359908i | −0.468507 | − | 0.883460i | \(-0.655208\pi\) |
0.530845 | + | 0.847469i | \(0.321875\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 18.0000i | − | 1.28245i | −0.767354 | − | 0.641223i | \(-0.778427\pi\) | ||
0.767354 | − | 0.641223i | \(-0.221573\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.50000 | + | 2.59808i | 0.106332 | + | 0.184173i | 0.914282 | − | 0.405079i | \(-0.132756\pi\) |
−0.807950 | + | 0.589252i | \(0.799423\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −6.00000 | + | 10.3923i | −0.423207 | + | 0.733017i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 6.92820 | − | 8.00000i | 0.486265 | − | 0.561490i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −6.92820 | + | 4.00000i | −0.481543 | + | 0.278019i | ||||
\(208\) | 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 | ||||||||
\(213\) | −8.66025 | + | 5.00000i | −0.593391 | + | 0.342594i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.79423 | + | 1.50000i | 0.529107 | + | 0.101827i | ||||
\(218\) | 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 | ||||||||
\(223\) | − | 17.0000i | − | 1.13840i | −0.822198 | − | 0.569202i | \(-0.807252\pi\) | ||
0.822198 | − | 0.569202i | \(-0.192748\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.73205 | + | 1.00000i | −0.114960 | + | 0.0663723i | −0.556378 | − | 0.830930i | \(-0.687809\pi\) |
0.441417 | + | 0.897302i | \(0.354476\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 13.0000 | − | 22.5167i | 0.859064 | − | 1.48794i | −0.0137585 | − | 0.999905i | \(-0.504380\pi\) |
0.872823 | − | 0.488037i | \(-0.162287\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −5.00000 | + | 1.73205i | −0.328976 | + | 0.113961i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3.46410 | − | 2.00000i | −0.226941 | − | 0.131024i | 0.382219 | − | 0.924072i | \(-0.375160\pi\) |
−0.609160 | + | 0.793047i | \(0.708493\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 7.00000i | 0.454699i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −18.0000 | −1.16432 | −0.582162 | − | 0.813073i | \(-0.697793\pi\) | ||||
−0.582162 | + | 0.813073i | \(0.697793\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.50000 | + | 9.52628i | 0.354286 | + | 0.613642i | 0.986996 | − | 0.160748i | \(-0.0513906\pi\) |
−0.632709 | + | 0.774389i | \(0.718057\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0.866025 | + | 0.500000i | 0.0555556 | + | 0.0320750i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.92820 | + | 4.00000i | 0.440831 | + | 0.254514i | ||||
\(248\) | 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 | ||||||||
\(253\) | 16.0000i | 1.00591i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −19.0526 | − | 11.0000i | −1.18847 | − | 0.686161i | −0.230508 | − | 0.973070i | \(-0.574039\pi\) |
−0.957958 | + | 0.286909i | \(0.907372\pi\) | |||||||
\(258\) | 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 | ||||||||
\(263\) | 19.0526 | − | 11.0000i | 1.17483 | − | 0.678289i | 0.220018 | − | 0.975496i | \(-0.429388\pi\) |
0.954813 | + | 0.297207i | \(0.0960551\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 10.0000i | 0.611990i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −6.00000 | − | 10.3923i | −0.365826 | − | 0.633630i | 0.623082 | − | 0.782157i | \(-0.285880\pi\) |
−0.988908 | + | 0.148527i | \(0.952547\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.00000 | + | 13.8564i | −0.485965 | + | 0.841717i | −0.999870 | − | 0.0161307i | \(-0.994865\pi\) |
0.513905 | + | 0.857847i | \(0.328199\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 5.19615 | + | 1.00000i | 0.314485 | + | 0.0605228i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.73205 | + | 1.00000i | −0.104069 | + | 0.0600842i | −0.551131 | − | 0.834419i | \(-0.685804\pi\) |
0.447062 | + | 0.894503i | \(0.352470\pi\) | |||||||
\(278\) | 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 | ||||||||
\(283\) | −13.8564 | + | 8.00000i | −0.823678 | + | 0.475551i | −0.851683 | − | 0.524057i | \(-0.824418\pi\) |
0.0280052 | + | 0.999608i | \(0.491084\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −10.3923 | + | 12.0000i | −0.613438 | + | 0.708338i | ||||
\(288\) | 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 | ||||||||
\(293\) | 6.00000i | 0.350524i | 0.984522 | + | 0.175262i | \(0.0560772\pi\) | ||||
−0.984522 | + | 0.175262i | \(0.943923\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.73205 | − | 1.00000i | 0.100504 | − | 0.0580259i | ||||
\(298\) | 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 | ||||||||
\(307\) | − | 7.00000i | − | 0.399511i | −0.979846 | − | 0.199756i | \(-0.935985\pi\) | ||
0.979846 | − | 0.199756i | \(-0.0640148\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 11.0000 | 0.625768 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 16.0000 | + | 27.7128i | 0.907277 | + | 1.57145i | 0.817832 | + | 0.575458i | \(0.195176\pi\) |
0.0894452 | + | 0.995992i | \(0.471491\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 23.3827 | + | 13.5000i | 1.32167 | + | 0.763065i | 0.983995 | − | 0.178198i | \(-0.0570269\pi\) |
0.337673 | + | 0.941263i | \(0.390360\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −29.4449 | − | 17.0000i | −1.65379 | − | 0.954815i | −0.975494 | − | 0.220024i | \(-0.929386\pi\) |
−0.678294 | − | 0.734791i | \(-0.737280\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.00000 | + | 6.92820i | 0.223957 | + | 0.387905i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 8.00000i | − | 0.445132i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −12.1244 | − | 7.00000i | −0.670478 | − | 0.387101i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −15.0000 | + | 5.19615i | −0.826977 | + | 0.286473i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.5000 | + | 23.3827i | −0.742027 | + | 1.28523i | 0.209544 | + | 0.977799i | \(0.432802\pi\) |
−0.951571 | + | 0.307429i | \(0.900531\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 7.79423 | − | 4.50000i | 0.427121 | − | 0.246598i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.00000i | 0.490261i | 0.969490 | + | 0.245131i | \(0.0788309\pi\) | ||||
−0.969490 | + | 0.245131i | \(0.921169\pi\) | |||||||
\(338\) | 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 | ||||||||
\(343\) | 15.5885 | + | 10.0000i | 0.841698 | + | 0.539949i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 22.5167 | − | 13.0000i | 1.20876 | − | 0.697877i | 0.246270 | − | 0.969201i | \(-0.420795\pi\) |
0.962488 | + | 0.271325i | \(0.0874617\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 34.0000 | 1.81998 | 0.909989 | − | 0.414632i | \(-0.136090\pi\) | ||||
0.909989 | + | 0.414632i | \(0.136090\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.00000 | −0.106752 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −13.8564 | + | 8.00000i | −0.737502 | + | 0.425797i | −0.821160 | − | 0.570697i | \(-0.806673\pi\) |
0.0836583 | + | 0.996495i | \(0.473340\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.73205 | − | 5.00000i | −0.0916698 | − | 0.264628i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −15.0000 | + | 25.9808i | −0.791670 | + | 1.37121i | 0.133263 | + | 0.991081i | \(0.457455\pi\) |
−0.924932 | + | 0.380131i | \(0.875879\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.50000 | + | 2.59808i | 0.0789474 | + | 0.136741i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 7.00000i | 0.367405i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −30.3109 | + | 17.5000i | −1.58222 | + | 0.913493i | −0.587680 | + | 0.809093i | \(0.699959\pi\) |
−0.994535 | + | 0.104399i | \(0.966708\pi\) | |||||||
\(368\) | 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 | ||||||||
\(373\) | −8.66025 | − | 5.00000i | −0.448411 | − | 0.258890i | 0.258748 | − | 0.965945i | \(-0.416690\pi\) |
−0.707159 | + | 0.707055i | \(0.750023\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 8.00000i | − | 0.412021i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −28.0000 | −1.43826 | −0.719132 | − | 0.694874i | \(-0.755460\pi\) | ||||
−0.719132 | + | 0.694874i | \(0.755460\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −8.50000 | − | 14.7224i | −0.435468 | − | 0.754253i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −27.7128 | − | 16.0000i | −1.41606 | − | 0.817562i | −0.420109 | − | 0.907474i | \(-0.638008\pi\) |
−0.995950 | + | 0.0899119i | \(0.971341\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.866025 | + | 0.500000i | 0.0440225 | + | 0.0254164i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 5.00000 | + | 8.66025i | 0.253510 | + | 0.439092i | 0.964490 | − | 0.264120i | \(-0.0850816\pi\) |
−0.710980 | + | 0.703213i | \(0.751748\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −16.0000 | −0.809155 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 22.0000i | 1.10975i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −23.3827 | − | 13.5000i | −1.17354 | − | 0.677546i | −0.219031 | − | 0.975718i | \(-0.570290\pi\) |
−0.954512 | + | 0.298172i | \(0.903623\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −8.00000 | − | 6.92820i | −0.400501 | − | 0.346844i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.00000 | − | 1.73205i | 0.0499376 | − | 0.0864945i | −0.839976 | − | 0.542623i | \(-0.817431\pi\) |
0.889914 | + | 0.456129i | \(0.150764\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.19615 | − | 3.00000i | 0.258839 | − | 0.149441i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 18.0000i | − | 0.892227i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.00000 | − | 12.1244i | −0.346128 | − | 0.599511i | 0.639430 | − | 0.768849i | \(-0.279170\pi\) |
−0.985558 | + | 0.169338i | \(0.945837\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −8.00000 | + | 13.8564i | −0.394611 | + | 0.683486i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 15.5885 | + | 3.00000i | 0.767058 | + | 0.147620i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.33013 | − | 2.50000i | 0.212047 | − | 0.122426i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −8.00000 | −0.390826 | −0.195413 | − | 0.980721i | \(-0.562605\pi\) | ||||
−0.195413 | + | 0.980721i | \(0.562605\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.0000 | 0.633581 | 0.316791 | − | 0.948495i | \(-0.397395\pi\) | ||||
0.316791 | + | 0.948495i | \(0.397395\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 5.19615 | − | 3.00000i | 0.252646 | − | 0.145865i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.866025 | + | 2.50000i | 0.0419099 | + | 0.120983i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.00000 | + | 3.46410i | −0.0965609 | + | 0.167248i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.00000i | 0.240285i | 0.992757 | + | 0.120142i | \(0.0383351\pi\) | ||||
−0.992757 | + | 0.120142i | \(0.961665\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −27.7128 | + | 16.0000i | −1.32568 | + | 0.765384i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.50000 | + | 9.52628i | −0.262501 | + | 0.454665i | −0.966906 | − | 0.255134i | \(-0.917881\pi\) |
0.704405 | + | 0.709798i | \(0.251214\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.50000 | − | 2.59808i | −0.309524 | − | 0.123718i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5.19615 | − | 3.00000i | −0.246877 | − | 0.142534i | 0.371457 | − | 0.928450i | \(-0.378858\pi\) |
−0.618333 | + | 0.785916i | \(0.712192\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 8.00000i | 0.378387i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −32.0000 | −1.51017 | −0.755087 | − | 0.655625i | \(-0.772405\pi\) | ||||
−0.755087 | + | 0.655625i | \(0.772405\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.00000 | − | 10.3923i | −0.282529 | − | 0.489355i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6.06218 | + | 3.50000i | 0.284826 | + | 0.164444i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −32.0429 | − | 18.5000i | −1.49891 | − | 0.865393i | −0.498906 | − | 0.866656i | \(-0.666265\pi\) |
−0.999999 | + | 0.00126243i | \(0.999598\pi\) | |||||||
\(458\) | 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 | ||||||||
\(463\) | 9.00000i | 0.418265i | 0.977887 | + | 0.209133i | \(0.0670641\pi\) | ||||
−0.977887 | + | 0.209133i | \(0.932936\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −5.19615 | − | 3.00000i | −0.240449 | − | 0.138823i | 0.374934 | − | 0.927052i | \(-0.377665\pi\) |
−0.615383 | + | 0.788228i | \(0.710999\pi\) | |||||||
\(468\) | 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 | ||||||||
\(473\) | 1.73205 | − | 1.00000i | 0.0796398 | − | 0.0459800i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.00000i | 0.0915737i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 16.0000 | + | 27.7128i | 0.731059 | + | 1.26623i | 0.956431 | + | 0.291958i | \(0.0943068\pi\) |
−0.225372 | + | 0.974273i | \(0.572360\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9.00000 | + | 15.5885i | −0.410365 | + | 0.710772i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −13.8564 | + | 16.0000i | −0.630488 | + | 0.728025i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9.52628 | + | 5.50000i | −0.431677 | + | 0.249229i | −0.700061 | − | 0.714083i | \(-0.746844\pi\) |
0.268384 | + | 0.963312i | \(0.413510\pi\) | |||||||
\(488\) | 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 | ||||||||
\(493\) | −6.92820 | + | 4.00000i | −0.312031 | + | 0.180151i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −17.3205 | + | 20.0000i | −0.776931 | + | 0.897123i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 18.0000 | − | 31.1769i | 0.805791 | − | 1.39567i | −0.109965 | − | 0.993935i | \(-0.535074\pi\) |
0.915756 | − | 0.401735i | \(-0.131593\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4.00000 | + | 6.92820i | 0.178707 | + | 0.309529i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 40.0000i | − | 1.78351i | −0.452517 | − | 0.891756i | \(-0.649474\pi\) | ||
0.452517 | − | 0.891756i | \(-0.350526\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −7.79423 | + | 4.50000i | −0.346154 | + | 0.199852i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 9.00000 | − | 15.5885i | 0.398918 | − | 0.690946i | −0.594675 | − | 0.803966i | \(-0.702719\pi\) |
0.993593 | + | 0.113020i | \(0.0360525\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.500000 | − | 2.59808i | 0.0221187 | − | 0.114932i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.46410 | + | 2.00000i | 0.152944 | + | 0.0883022i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 12.0000i | − | 0.527759i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 6.00000 | 0.263371 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.00000 | + | 5.19615i | 0.131432 | + | 0.227648i | 0.924229 | − | 0.381839i | \(-0.124709\pi\) |
−0.792797 | + | 0.609486i | \(0.791376\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.866025 | + | 0.500000i | 0.0378686 | + | 0.0218635i | 0.518815 | − | 0.854887i | \(-0.326373\pi\) |
−0.480946 | + | 0.876750i | \(0.659707\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −5.19615 | − | 3.00000i | −0.226348 | − | 0.130682i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 20.5000 | + | 35.5070i | 0.891304 | + | 1.54378i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6.00000 | −0.260378 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 12.0000i | 0.519778i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −13.8564 | − | 8.00000i | −0.597948 | − | 0.345225i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −11.0000 | + | 8.66025i | −0.473804 | + | 0.373024i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.00000 | − | 8.66025i | 0.214967 | − | 0.372333i | −0.738296 | − | 0.674477i | \(-0.764369\pi\) |
0.953262 | + | 0.302144i | \(0.0977023\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 12.9904 | − | 7.50000i | 0.557471 | − | 0.321856i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12.0000i | 0.513083i | 0.966533 | + | 0.256541i | \(0.0825830\pi\) | ||||
−0.966533 | + | 0.256541i | \(0.917417\pi\) | |||||||
\(548\) | 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 | ||||||||
\(553\) | 6.06218 | + | 17.5000i | 0.257790 | + | 0.744176i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 15.5885 | − | 9.00000i | 0.660504 | − | 0.381342i | −0.131965 | − | 0.991254i | \(-0.542129\pi\) |
0.792469 | + | 0.609912i | \(0.208795\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.00000 | −0.0845910 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.00000 | 0.168880 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 29.4449 | − | 17.0000i | 1.24095 | − | 0.716465i | 0.271665 | − | 0.962392i | \(-0.412426\pi\) |
0.969288 | + | 0.245927i | \(0.0790925\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.59808 | + | 0.500000i | 0.109109 | + | 0.0209980i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −2.00000 | + | 3.46410i | −0.0838444 | + | 0.145223i | −0.904898 | − | 0.425628i | \(-0.860053\pi\) |
0.821054 | + | 0.570851i | \(0.193387\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.00000 | − | 3.46410i | −0.0836974 | − | 0.144968i | 0.821138 | − | 0.570730i | \(-0.193340\pi\) |
−0.904835 | + | 0.425762i | \(0.860006\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4.00000i | 0.167102i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 26.8468 | − | 15.5000i | 1.11765 | − | 0.645273i | 0.176847 | − | 0.984238i | \(-0.443410\pi\) |
0.940799 | + | 0.338965i | \(0.110077\pi\) | |||||||
\(578\) | 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 | ||||||||
\(583\) | 3.46410 | + | 2.00000i | 0.143468 | + | 0.0828315i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 42.0000i | − | 1.73353i | −0.498721 | − | 0.866763i | \(-0.666197\pi\) | ||
0.498721 | − | 0.866763i | \(-0.333803\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −12.0000 | −0.494451 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 9.00000 | + | 15.5885i | 0.370211 | + | 0.641223i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −20.7846 | − | 12.0000i | −0.853522 | − | 0.492781i | 0.00831589 | − | 0.999965i | \(-0.497353\pi\) |
−0.861838 | + | 0.507184i | \(0.830686\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2.59808 | − | 1.50000i | −0.106332 | − | 0.0613909i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 24.0000 | + | 41.5692i | 0.980613 | + | 1.69847i | 0.660006 | + | 0.751260i | \(0.270554\pi\) |
0.320607 | + | 0.947212i | \(0.396113\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −26.0000 | −1.06056 | −0.530281 | − | 0.847822i | \(-0.677914\pi\) | ||||
−0.530281 | + | 0.847822i | \(0.677914\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 12.0000i | − | 0.488678i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −37.2391 | − | 21.5000i | −1.51149 | − | 0.872658i | −0.999910 | − | 0.0134214i | \(-0.995728\pi\) |
−0.511578 | − | 0.859237i | \(-0.670939\pi\) | |||||||
\(608\) | 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 | ||||||||
\(613\) | 25.9808 | − | 15.0000i | 1.04935 | − | 0.605844i | 0.126885 | − | 0.991917i | \(-0.459502\pi\) |
0.922468 | + | 0.386073i | \(0.126169\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 14.0000i | 0.563619i | 0.959470 | + | 0.281809i | \(0.0909346\pi\) | ||||
−0.959470 | + | 0.281809i | \(0.909065\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −15.5000 | − | 26.8468i | −0.622998 | − | 1.07906i | −0.988924 | − | 0.148420i | \(-0.952581\pi\) |
0.365927 | − | 0.930644i | \(-0.380752\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.00000 | − | 6.92820i | 0.160514 | − | 0.278019i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 8.66025 | + | 25.0000i | 0.346966 | + | 1.00160i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 6.92820 | − | 4.00000i | 0.276686 | − | 0.159745i | ||||
\(628\) | 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 | ||||||||
\(633\) | 7.79423 | − | 4.50000i | 0.309793 | − | 0.178859i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 13.8564 | − | 2.00000i | 0.549011 | − | 0.0792429i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 5.00000 | − | 8.66025i | 0.197797 | − | 0.342594i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5.00000 | − | 8.66025i | −0.197488 | − | 0.342059i | 0.750225 | − | 0.661182i | \(-0.229945\pi\) |
−0.947713 | + | 0.319123i | \(0.896612\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 5.00000i | − | 0.197181i | −0.995128 | − | 0.0985904i | \(-0.968567\pi\) | ||
0.995128 | − | 0.0985904i | \(-0.0314334\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −5.19615 | + | 3.00000i | −0.204282 | + | 0.117942i | −0.598651 | − | 0.801010i | \(-0.704296\pi\) |
0.394369 | + | 0.918952i | \(0.370963\pi\) | |||||||
\(648\) | 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 | ||||||||
\(653\) | 22.5167 | + | 13.0000i | 0.881145 | + | 0.508729i | 0.871036 | − | 0.491220i | \(-0.163449\pi\) |
0.0101092 | + | 0.999949i | \(0.496782\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.00000i | 0.0390137i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −42.0000 | −1.63609 | −0.818044 | − | 0.575156i | \(-0.804941\pi\) | ||||
−0.818044 | + | 0.575156i | \(0.804941\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.50000 | − | 9.52628i | −0.213925 | − | 0.370529i | 0.739014 | − | 0.673690i | \(-0.235292\pi\) |
−0.952940 | + | 0.303160i | \(0.901958\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3.46410 | − | 2.00000i | −0.134535 | − | 0.0776736i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 27.7128 | + | 16.0000i | 1.07304 | + | 0.619522i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 8.50000 | + | 14.7224i | 0.328629 | + | 0.569202i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.00000 | −0.0772091 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.00000i | 0.346925i | 0.984841 | + | 0.173462i | \(0.0554955\pi\) | ||||
−0.984841 | + | 0.173462i | \(0.944505\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 27.7128 | + | 16.0000i | 1.06509 | + | 0.614930i | 0.926836 | − | 0.375467i | \(-0.122518\pi\) |
0.138254 | + | 0.990397i | \(0.455851\pi\) | |||||||
\(678\) | 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 | ||||||||
\(683\) | 5.19615 | − | 3.00000i | 0.198825 | − | 0.114792i | −0.397282 | − | 0.917697i | \(-0.630047\pi\) |
0.596107 | + | 0.802905i | \(0.296713\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 26.0000i | 0.991962i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.00000 | − | 3.46410i | −0.0761939 | − | 0.131972i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −13.5000 | + | 23.3827i | −0.513564 | + | 0.889519i | 0.486312 | + | 0.873785i | \(0.338342\pi\) |
−0.999876 | + | 0.0157341i | \(0.994991\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.46410 | − | 4.00000i | 0.131590 | − | 0.151947i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 10.3923 | − | 6.00000i | 0.393637 | − | 0.227266i | ||||
\(698\) | 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 | ||||||||
\(703\) | 31.1769 | − | 18.0000i | 1.17586 | − | 0.678883i | ||||
\(704\) | 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 | \(-0.899559\pi\) |
0.744071 | + | 0.668101i | \(0.232892\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.50000 | − | 6.06218i | −0.131260 | − | 0.227349i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 24.0000i | 0.898807i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 15.5885 | − | 9.00000i | 0.582162 | − | 0.336111i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 22.0000 | − | 38.1051i | 0.820462 | − | 1.42108i | −0.0848774 | − | 0.996391i | \(-0.527050\pi\) |
0.905339 | − | 0.424690i | \(-0.139617\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 27.5000 | − | 9.52628i | 1.02415 | − | 0.354777i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −9.52628 | − | 5.50000i | −0.354286 | − | 0.204547i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8.00000i | 0.296704i | 0.988935 | + | 0.148352i | \(0.0473968\pi\) | ||||
−0.988935 | + | 0.148352i | \(0.952603\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.00000 | + | 1.73205i | 0.0369863 | + | 0.0640622i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −30.3109 | − | 17.5000i | −1.11956 | − | 0.646377i | −0.178270 | − | 0.983982i | \(-0.557050\pi\) |
−0.941288 | + | 0.337604i | \(0.890383\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −20.7846 | − | 12.0000i | −0.765611 | − | 0.442026i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 20.5000 | + | 35.5070i | 0.754105 | + | 1.30615i | 0.945818 | + | 0.324697i | \(0.105262\pi\) |
−0.191714 | + | 0.981451i | \(0.561404\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −8.00000 | −0.293887 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 12.0000i | 0.440237i | 0.975473 | + | 0.220119i | \(0.0706445\pi\) | ||||
−0.975473 | + | 0.220119i | \(0.929356\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −15.5885 | − | 9.00000i | −0.570352 | − | 0.329293i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12.5000 | + | 21.6506i | −0.456131 | + | 0.790043i | −0.998752 | − | 0.0499348i | \(-0.984099\pi\) |
0.542621 | + | 0.839978i | \(0.317432\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 13.0000i | 0.472493i | 0.971693 | + | 0.236247i | \(0.0759173\pi\) | ||||
−0.971693 | + | 0.236247i | \(0.924083\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −8.00000 | − | 13.8564i | −0.290382 | − | 0.502956i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 16.0000 | − | 27.7128i | 0.580000 | − | 1.00459i | −0.415479 | − | 0.909603i | \(-0.636386\pi\) |
0.995479 | − | 0.0949859i | \(-0.0302806\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −36.3731 | − | 7.00000i | −1.31679 | − | 0.253417i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 10.3923 | − | 6.00000i | 0.375244 | − | 0.216647i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 29.0000 | 1.04577 | 0.522883 | − | 0.852404i | \(-0.324856\pi\) | ||||
0.522883 | + | 0.852404i | \(0.324856\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 22.0000 | 0.792311 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −24.2487 | + | 14.0000i | −0.872166 | + | 0.503545i | −0.868067 | − | 0.496447i | \(-0.834638\pi\) |
−0.00409826 | + | 0.999992i | \(0.501305\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 15.5885 | − | 18.0000i | 0.559233 | − | 0.645746i | ||||
\(778\) | 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 | ||||||||
\(783\) | − | 4.00000i | − | 0.142948i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 9.52628 | − | 5.50000i | 0.339575 | − | 0.196054i | −0.320509 | − | 0.947245i | \(-0.603854\pi\) |
0.660084 | + | 0.751192i | \(0.270521\pi\) | |||||||
\(788\) | 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 | ||||||||
\(793\) | 1.73205 | + | 1.00000i | 0.0615069 | + | 0.0355110i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 12.0000i | − | 0.425062i | −0.977154 | − | 0.212531i | \(-0.931829\pi\) | ||
0.977154 | − | 0.212531i | \(-0.0681706\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 12.0000 | 0.424529 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −5.00000 | − | 8.66025i | −0.176666 | − | 0.305995i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.73205 | + | 1.00000i | 0.0611227 | + | 0.0352892i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 10.3923 | + | 6.00000i | 0.365826 | + | 0.211210i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −14.0000 | − | 24.2487i | −0.492214 | − | 0.852539i | 0.507746 | − | 0.861507i | \(-0.330479\pi\) |
−0.999960 | + | 0.00896753i | \(0.997146\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 43.0000 | 1.50993 | 0.754967 | − | 0.655763i | \(-0.227653\pi\) | ||||
0.754967 | + | 0.655763i | \(0.227653\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 16.0000i | − | 0.561144i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.46410 | + | 2.00000i | 0.121194 | + | 0.0699711i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −5.00000 | + | 1.73205i | −0.174714 | + | 0.0605228i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 4.00000 | − | 6.92820i | 0.139601 | − | 0.241796i | −0.787745 | − | 0.616002i | \(-0.788751\pi\) |
0.927346 | + | 0.374206i | \(0.122085\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 12.9904 | − | 7.50000i | 0.452816 | − | 0.261434i | −0.256203 | − | 0.966623i | \(-0.582471\pi\) |
0.709019 | + | 0.705190i | \(0.249138\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 14.0000i | − | 0.486828i | −0.969923 | − | 0.243414i | \(-0.921733\pi\) | ||
0.969923 | − | 0.243414i | \(-0.0782673\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 4.50000 | + | 7.79423i | 0.156291 | + | 0.270705i | 0.933529 | − | 0.358503i | \(-0.116713\pi\) |
−0.777237 | + | 0.629208i | \(0.783379\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.00000 | − | 1.73205i | 0.0346896 | − | 0.0600842i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −8.66025 | − | 11.0000i | −0.300060 | − | 0.381127i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.59808 | − | 1.50000i | 0.0898027 | − | 0.0518476i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 34.0000 | 1.17381 | 0.586905 | − | 0.809656i | \(-0.300346\pi\) | ||||
0.586905 | + | 0.809656i | \(0.300346\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13.0000 | −0.448276 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −25.9808 | + | 15.0000i | −0.894825 | + | 0.516627i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6.06218 | + | 17.5000i | 0.208299 | + | 0.601307i | ||||
\(848\) | 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 | ||||||||
\(853\) | − | 7.00000i | − | 0.239675i | −0.992793 | − | 0.119838i | \(-0.961763\pi\) | ||
0.992793 | − | 0.119838i | \(-0.0382374\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −34.6410 | + | 20.0000i | −1.18331 | + | 0.683187i | −0.956779 | − | 0.290816i | \(-0.906073\pi\) |
−0.226536 | + | 0.974003i | \(0.572740\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 14.0000 | − | 24.2487i | 0.477674 | − | 0.827355i | −0.521999 | − | 0.852946i | \(-0.674813\pi\) |
0.999672 | + | 0.0255910i | \(0.00814674\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.00000 | − | 15.5885i | 0.102240 | − | 0.531253i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 12.1244 | + | 7.00000i | 0.412718 | + | 0.238283i | 0.691957 | − | 0.721939i | \(-0.256749\pi\) |
−0.279239 | + | 0.960222i | \(0.590082\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 13.0000i | − | 0.441503i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −14.0000 | −0.474917 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 12.0000 | + | 20.7846i | 0.406604 | + | 0.704260i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 4.33013 | + | 2.50000i | 0.146553 | + | 0.0846122i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −19.9186 | − | 11.5000i | −0.672603 | − | 0.388327i | 0.124459 | − | 0.992225i | \(-0.460280\pi\) |
−0.797062 | + | 0.603897i | \(0.793614\pi\) | |||||||
\(878\) | 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 | ||||||||
\(883\) | 4.00000i | 0.134611i | 0.997732 | + | 0.0673054i | \(0.0214402\pi\) | ||||
−0.997732 | + | 0.0673054i | \(0.978560\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 29.4449 | + | 17.0000i | 0.988662 | + | 0.570804i | 0.904874 | − | 0.425679i | \(-0.139965\pi\) |
0.0837878 | + | 0.996484i | \(0.473298\pi\) | |||||||
\(888\) | 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 | ||||||||
\(893\) | 20.7846 | − | 12.0000i | 0.695530 | − | 0.401565i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 16.0000i | 0.534224i | ||||||||
\(898\) | 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 | ||||||||
\(903\) | 2.59808 | + | 0.500000i | 0.0864586 | + | 0.0166390i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 16.4545 | − | 9.50000i | 0.546362 | − | 0.315442i | −0.201291 | − | 0.979531i | \(-0.564514\pi\) |
0.747653 | + | 0.664089i | \(0.231180\pi\) | |||||||
\(908\) | 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 | ||||||||
\(913\) | −31.1769 | + | 18.0000i | −1.03181 | + | 0.595713i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 19.0526 | + | 55.0000i | 0.629171 | + | 1.81626i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −5.50000 | + | 9.52628i | −0.181428 | + | 0.314243i | −0.942367 | − | 0.334581i | \(-0.891405\pi\) |
0.760939 | + | 0.648824i | \(0.224739\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3.50000 | + | 6.06218i | 0.115329 | + | 0.199756i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 20.0000i | 0.658308i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −9.52628 | + | 5.50000i | −0.312884 | + | 0.180644i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 23.0000 | − | 39.8372i | 0.754606 | − | 1.30702i | −0.190965 | − | 0.981597i | \(-0.561162\pi\) |
0.945570 | − | 0.325418i | \(-0.105505\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −26.0000 | − | 10.3923i | −0.852116 | − | 0.340594i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −27.7128 | − | 16.0000i | −0.907277 | − | 0.523816i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 19.0000i | 0.620703i | 0.950622 | + | 0.310351i | \(0.100447\pi\) | ||||
−0.950622 | + | 0.310351i | \(0.899553\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −27.0000 | −0.881112 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 9.00000 | + | 15.5885i | 0.293392 | + | 0.508169i | 0.974609 | − | 0.223912i | \(-0.0718827\pi\) |
−0.681218 | + | 0.732081i | \(0.738549\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −41.5692 | − | 24.0000i | −1.35368 | − | 0.781548i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 43.3013 | + | 25.0000i | 1.40710 | + | 0.812391i | 0.995108 | − | 0.0987955i | \(-0.0314990\pi\) |
0.411994 | + | 0.911186i | \(0.364832\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.00000 | − | 1.73205i | −0.0324614 | − | 0.0562247i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 34.0000 | 1.10253 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 52.0000i | 1.68445i | 0.539130 | + | 0.842223i | \(0.318753\pi\) | ||||
−0.539130 | + | 0.842223i | \(0.681247\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −6.92820 | − | 4.00000i | −0.223957 | − | 0.129302i | ||||
\(958\) | 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 | ||||||||
\(967\) | 31.0000i | 0.996893i | 0.866921 | + | 0.498446i | \(0.166096\pi\) | ||||
−0.866921 | + | 0.498446i | \(0.833904\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4.00000 | + | 6.92820i | 0.128499 | + | 0.222566i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 22.0000 | − | 38.1051i | 0.706014 | − | 1.22285i | −0.260311 | − | 0.965525i | \(-0.583825\pi\) |
0.966324 | − | 0.257327i | \(-0.0828416\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8.66025 | − | 10.0000i | 0.277635 | − | 0.320585i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −10.3923 | + | 6.00000i | −0.332479 | + | 0.191957i | −0.656941 | − | 0.753942i | \(-0.728150\pi\) |
0.324462 | + | 0.945899i | \(0.394817\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −20.0000 | −0.639203 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 14.0000 | 0.446986 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 15.5885 | − | 9.00000i | 0.497195 | − | 0.287055i | −0.230360 | − | 0.973106i | \(-0.573990\pi\) |
0.727554 | + | 0.686050i | \(0.240657\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 10.3923 | − | 12.0000i | 0.330791 | − | 0.381964i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.00000 | − | 6.92820i | 0.127193 | − | 0.220304i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −15.5000 | − | 26.8468i | −0.492374 | − | 0.852816i | 0.507588 | − | 0.861600i | \(-0.330537\pi\) |
−0.999961 | + | 0.00878379i | \(0.997204\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 27.0000i | − | 0.856819i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 26.8468 | − | 15.5000i | 0.850246 | − | 0.490890i | −0.0104877 | − | 0.999945i | \(-0.503338\pi\) |
0.860734 | + | 0.509055i | \(0.170005\pi\) | |||||||
\(998\) | 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.bc.b.1549.1 | 4 | ||
5.2 | odd | 4 | 2100.2.q.e.1801.1 | yes | 2 | ||
5.3 | odd | 4 | 2100.2.q.c.1801.1 | yes | 2 | ||
5.4 | even | 2 | inner | 2100.2.bc.b.1549.2 | 4 | ||
7.4 | even | 3 | inner | 2100.2.bc.b.949.2 | 4 | ||
35.4 | even | 6 | inner | 2100.2.bc.b.949.1 | 4 | ||
35.18 | odd | 12 | 2100.2.q.c.1201.1 | ✓ | 2 | ||
35.32 | odd | 12 | 2100.2.q.e.1201.1 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2100.2.q.c.1201.1 | ✓ | 2 | 35.18 | odd | 12 | ||
2100.2.q.c.1801.1 | yes | 2 | 5.3 | odd | 4 | ||
2100.2.q.e.1201.1 | yes | 2 | 35.32 | odd | 12 | ||
2100.2.q.e.1801.1 | yes | 2 | 5.2 | odd | 4 | ||
2100.2.bc.b.949.1 | 4 | 35.4 | even | 6 | inner | ||
2100.2.bc.b.949.2 | 4 | 7.4 | even | 3 | inner | ||
2100.2.bc.b.1549.1 | 4 | 1.1 | even | 1 | trivial | ||
2100.2.bc.b.1549.2 | 4 | 5.4 | even | 2 | inner |