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: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.49787136.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 3x^{6} + 5x^{4} + 12x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1549.1 | ||
Root | \(1.09445 - 0.895644i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2100.1549 |
Dual form | 2100.2.bc.h.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 | ||||||||
\(7\) | −2.29129 | + | 1.32288i | −0.866025 | + | 0.500000i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.500000 | − | 0.866025i | 0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.177124 | + | 0.306788i | 0.0534050 | + | 0.0925002i | 0.891492 | − | 0.453036i | \(-0.149659\pi\) |
−0.838087 | + | 0.545537i | \(0.816326\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000i | 0.277350i | 0.990338 | + | 0.138675i | \(0.0442844\pi\) | ||||
−0.990338 | + | 0.138675i | \(0.955716\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.15731 | + | 1.82288i | −0.765761 | + | 0.442112i | −0.831360 | − | 0.555734i | \(-0.812437\pi\) |
0.0655994 | + | 0.997846i | \(0.479104\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.322876 | − | 0.559237i | 0.0740728 | − | 0.128298i | −0.826610 | − | 0.562775i | \(-0.809734\pi\) |
0.900683 | + | 0.434478i | \(0.143067\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.32288 | − | 2.29129i | 0.288675 | − | 0.500000i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.73205 | + | 1.00000i | 0.361158 | + | 0.208514i | 0.669588 | − | 0.742732i | \(-0.266471\pi\) |
−0.308431 | + | 0.951247i | \(0.599804\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.29150 | 0.611217 | 0.305608 | − | 0.952157i | \(-0.401140\pi\) | ||||
0.305608 | + | 0.952157i | \(0.401140\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.00000 | − | 3.46410i | −0.359211 | − | 0.622171i | 0.628619 | − | 0.777714i | \(-0.283621\pi\) |
−0.987829 | + | 0.155543i | \(0.950287\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.306788 | − | 0.177124i | −0.0534050 | − | 0.0308334i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.98450 | − | 1.14575i | −0.326250 | − | 0.188360i | 0.327925 | − | 0.944704i | \(-0.393651\pi\) |
−0.654175 | + | 0.756343i | \(0.726984\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.500000 | − | 0.866025i | −0.0800641 | − | 0.138675i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.64575 | −0.881718 | −0.440859 | − | 0.897576i | \(-0.645326\pi\) | ||||
−0.440859 | + | 0.897576i | \(0.645326\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.29150i | 0.501949i | 0.967994 | + | 0.250975i | \(0.0807511\pi\) | ||||
−0.967994 | + | 0.250975i | \(0.919249\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −11.2040 | − | 6.46863i | −1.63427 | − | 0.943546i | −0.982755 | − | 0.184910i | \(-0.940801\pi\) |
−0.651515 | − | 0.758636i | \(-0.725866\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.50000 | − | 6.06218i | 0.500000 | − | 0.866025i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.82288 | − | 3.15731i | 0.255254 | − | 0.442112i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.62141 | − | 3.82288i | 0.909521 | − | 0.525112i | 0.0292442 | − | 0.999572i | \(-0.490690\pi\) |
0.880277 | + | 0.474460i | \(0.157357\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.645751i | 0.0855319i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.468627 | − | 0.811686i | −0.0610100 | − | 0.105672i | 0.833907 | − | 0.551905i | \(-0.186099\pi\) |
−0.894917 | + | 0.446232i | \(0.852765\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.79150 | − | 10.0312i | 0.741526 | − | 1.28436i | −0.210274 | − | 0.977642i | \(-0.567436\pi\) |
0.951800 | − | 0.306718i | \(-0.0992309\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.64575i | 0.333333i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.87386 | + | 3.96863i | −0.839776 | + | 0.484845i | −0.857188 | − | 0.515003i | \(-0.827791\pi\) |
0.0174120 | + | 0.999848i | \(0.494457\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.00000 | −0.240772 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.29150 | −0.865342 | −0.432671 | − | 0.901552i | \(-0.642429\pi\) | ||||
−0.432671 | + | 0.901552i | \(0.642429\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.71655 | − | 2.14575i | 0.434989 | − | 0.251141i | −0.266481 | − | 0.963840i | \(-0.585861\pi\) |
0.701470 | + | 0.712699i | \(0.252527\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.811686 | − | 0.468627i | −0.0925002 | − | 0.0534050i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.677124 | + | 1.17281i | −0.0761824 | + | 0.131952i | −0.901600 | − | 0.432571i | \(-0.857606\pi\) |
0.825417 | + | 0.564523i | \(0.190940\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 1.64575i | − | 0.180645i | −0.995913 | − | 0.0903223i | \(-0.971210\pi\) | ||
0.995913 | − | 0.0903223i | \(-0.0287897\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.85052 | + | 1.64575i | −0.305608 | + | 0.176443i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.46863 | − | 6.00784i | 0.367674 | − | 0.636830i | −0.621528 | − | 0.783392i | \(-0.713488\pi\) |
0.989201 | + | 0.146563i | \(0.0468210\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.32288 | − | 2.29129i | −0.138675 | − | 0.240192i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.46410 | + | 2.00000i | 0.359211 | + | 0.207390i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 3.70850i | − | 0.376541i | −0.982117 | − | 0.188270i | \(-0.939712\pi\) | ||
0.982117 | − | 0.188270i | \(-0.0602881\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.354249 | 0.0356033 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.46863 | − | 4.27579i | −0.245638 | − | 0.425457i | 0.716673 | − | 0.697409i | \(-0.245664\pi\) |
−0.962311 | + | 0.271953i | \(0.912331\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.0543397 | − | 0.0313730i | −0.00535425 | − | 0.00309128i | 0.497320 | − | 0.867567i | \(-0.334317\pi\) |
−0.502675 | + | 0.864476i | \(0.667651\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −14.0545 | − | 8.11438i | −1.35870 | − | 0.784447i | −0.369252 | − | 0.929329i | \(-0.620386\pi\) |
−0.989449 | + | 0.144883i | \(0.953720\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.79150 | − | 10.0312i | −0.554725 | − | 0.960812i | −0.997925 | − | 0.0643895i | \(-0.979490\pi\) |
0.443200 | − | 0.896423i | \(-0.353843\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.29150 | 0.217500 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 8.58301i | − | 0.807421i | −0.914887 | − | 0.403711i | \(-0.867720\pi\) | ||
0.914887 | − | 0.403711i | \(-0.132280\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.866025 | + | 0.500000i | 0.0800641 | + | 0.0462250i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.82288 | − | 8.35347i | 0.442112 | − | 0.765761i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.43725 | − | 9.41760i | 0.494296 | − | 0.856145i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 4.88936 | − | 2.82288i | 0.440859 | − | 0.254530i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.35425i | 0.120170i | 0.998193 | + | 0.0600851i | \(0.0191372\pi\) | ||||
−0.998193 | + | 0.0600851i | \(0.980863\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.64575 | − | 2.85052i | −0.144900 | − | 0.250975i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.291503 | + | 0.504897i | −0.0254687 | + | 0.0441131i | −0.878479 | − | 0.477781i | \(-0.841441\pi\) |
0.853010 | + | 0.521894i | \(0.174774\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.70850i | 0.148146i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.11847 | + | 0.645751i | −0.0955577 | + | 0.0551703i | −0.547017 | − | 0.837121i | \(-0.684237\pi\) |
0.451460 | + | 0.892292i | \(0.350903\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −15.9373 | −1.35178 | −0.675890 | − | 0.737002i | \(-0.736241\pi\) | ||||
−0.675890 | + | 0.737002i | \(0.736241\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 12.9373 | 1.08951 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.306788 | + | 0.177124i | −0.0256549 | + | 0.0148119i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 7.00000i | 0.577350i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.46863 | − | 4.27579i | 0.202238 | − | 0.350286i | −0.747011 | − | 0.664811i | \(-0.768512\pi\) |
0.949249 | + | 0.314525i | \(0.101845\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.67712 | + | 9.83307i | 0.461998 | + | 0.800204i | 0.999060 | − | 0.0433387i | \(-0.0137995\pi\) |
−0.537063 | + | 0.843542i | \(0.680466\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.64575i | 0.294742i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −14.7224 | + | 8.50000i | −1.17498 | + | 0.678374i | −0.954847 | − | 0.297097i | \(-0.903982\pi\) |
−0.220131 | + | 0.975470i | \(0.570648\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.82288 | + | 6.62141i | −0.303174 | + | 0.525112i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.29150 | −0.417029 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 14.9205 | + | 8.61438i | 1.16867 | + | 0.674730i | 0.953366 | − | 0.301818i | \(-0.0975933\pi\) |
0.215301 | + | 0.976548i | \(0.430927\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 19.5203i | − | 1.51052i | −0.655424 | − | 0.755262i | \(-0.727510\pi\) | ||
0.655424 | − | 0.755262i | \(-0.272490\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.0000 | 0.923077 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.322876 | − | 0.559237i | −0.0246909 | − | 0.0427659i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −17.8254 | − | 10.2915i | −1.35524 | − | 0.782448i | −0.366263 | − | 0.930512i | \(-0.619363\pi\) |
−0.988978 | + | 0.148063i | \(0.952696\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.811686 | + | 0.468627i | 0.0610100 | + | 0.0352242i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −11.6458 | − | 20.1710i | −0.870444 | − | 1.50765i | −0.861538 | − | 0.507693i | \(-0.830498\pi\) |
−0.00890653 | − | 0.999960i | \(-0.502835\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.5830 | 1.08395 | 0.541973 | − | 0.840396i | \(-0.317677\pi\) | ||||
0.541973 | + | 0.840396i | \(0.317677\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 11.5830i | 0.856240i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.11847 | − | 0.645751i | −0.0817909 | − | 0.0472220i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.32288 | − | 2.29129i | −0.0962250 | − | 0.166667i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.76013 | + | 11.7089i | −0.489146 | + | 0.847225i | −0.999922 | − | 0.0124883i | \(-0.996025\pi\) |
0.510776 | + | 0.859714i | \(0.329358\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 13.8564 | − | 8.00000i | 0.997406 | − | 0.575853i | 0.0899262 | − | 0.995948i | \(-0.471337\pi\) |
0.907480 | + | 0.420096i | \(0.138004\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.70850i | 0.620455i | 0.950662 | + | 0.310227i | \(0.100405\pi\) | ||||
−0.950662 | + | 0.310227i | \(0.899595\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.322876 | + | 0.559237i | 0.0228880 | + | 0.0396433i | 0.877243 | − | 0.480047i | \(-0.159381\pi\) |
−0.854355 | + | 0.519691i | \(0.826047\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.96863 | − | 6.87386i | 0.279925 | − | 0.484845i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −7.54178 | + | 4.35425i | −0.529329 | + | 0.305608i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.73205 | − | 1.00000i | 0.120386 | − | 0.0695048i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.228757 | 0.0158234 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.06275 | −0.142005 | −0.0710026 | − | 0.997476i | \(-0.522620\pi\) | ||||
−0.0710026 | + | 0.997476i | \(0.522620\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 6.31463 | − | 3.64575i | 0.432671 | − | 0.249803i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9.16515 | + | 5.29150i | 0.622171 | + | 0.359211i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.14575 | + | 3.71655i | −0.144996 | + | 0.251141i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.82288 | − | 3.15731i | −0.122620 | − | 0.212384i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 13.9373i | 0.933308i | 0.884440 | + | 0.466654i | \(0.154541\pi\) | ||||
−0.884440 | + | 0.466654i | \(0.845459\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 7.54178 | − | 4.35425i | 0.500566 | − | 0.289002i | −0.228382 | − | 0.973572i | \(-0.573343\pi\) |
0.728947 | + | 0.684570i | \(0.240010\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10.1458 | + | 17.5730i | −0.670450 | + | 1.16125i | 0.307326 | + | 0.951604i | \(0.400566\pi\) |
−0.977777 | + | 0.209650i | \(0.932768\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.937254 | 0.0616668 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −20.9827 | − | 12.1144i | −1.37462 | − | 0.793639i | −0.383118 | − | 0.923700i | \(-0.625150\pi\) |
−0.991506 | + | 0.130060i | \(0.958483\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 1.35425i | − | 0.0879679i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 9.41699 | 0.609135 | 0.304567 | − | 0.952491i | \(-0.401488\pi\) | ||||
0.304567 | + | 0.952491i | \(0.401488\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.145751 | + | 0.252449i | 0.00938867 | + | 0.0162616i | 0.870682 | − | 0.491847i | \(-0.163678\pi\) |
−0.861293 | + | 0.508109i | \(0.830345\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0.866025 | + | 0.500000i | 0.0555556 | + | 0.0320750i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.559237 | + | 0.322876i | 0.0355834 | + | 0.0205441i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.822876 | + | 1.42526i | 0.0521476 | + | 0.0903223i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −28.8118 | −1.81858 | −0.909291 | − | 0.416161i | \(-0.863375\pi\) | ||||
−0.909291 | + | 0.416161i | \(0.863375\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.708497i | 0.0445428i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −15.2817 | − | 8.82288i | −0.953244 | − | 0.550356i | −0.0591571 | − | 0.998249i | \(-0.518841\pi\) |
−0.894087 | + | 0.447893i | \(0.852175\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.06275 | 0.376721 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.64575 | − | 2.85052i | 0.101869 | − | 0.176443i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 20.7846 | − | 12.0000i | 1.28163 | − | 0.739952i | 0.304487 | − | 0.952517i | \(-0.401515\pi\) |
0.977147 | + | 0.212565i | \(0.0681817\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.93725i | 0.424553i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 10.1144 | + | 17.5186i | 0.616685 | + | 1.06813i | 0.990086 | + | 0.140459i | \(0.0448579\pi\) |
−0.373402 | + | 0.927670i | \(0.621809\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.35425 | − | 2.34563i | 0.0822647 | − | 0.142487i | −0.821958 | − | 0.569549i | \(-0.807118\pi\) |
0.904222 | + | 0.427062i | \(0.140451\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.29129 | + | 1.32288i | 0.138675 | + | 0.0800641i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 21.6506 | − | 12.5000i | 1.30086 | − | 0.751052i | 0.320309 | − | 0.947313i | \(-0.396213\pi\) |
0.980552 | + | 0.196261i | \(0.0628800\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4.00000 | −0.239474 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −22.2288 | −1.32606 | −0.663028 | − | 0.748594i | \(-0.730729\pi\) | ||||
−0.663028 | + | 0.748594i | \(0.730729\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.64671 | + | 3.26013i | −0.335662 | + | 0.193795i | −0.658352 | − | 0.752710i | \(-0.728746\pi\) |
0.322690 | + | 0.946505i | \(0.395413\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 12.9360 | − | 7.46863i | 0.763590 | − | 0.440859i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.85425 | + | 3.21165i | −0.109073 | + | 0.188921i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.85425 | + | 3.21165i | 0.108698 | + | 0.188270i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 9.87451i | − | 0.576875i | −0.957499 | − | 0.288437i | \(-0.906864\pi\) | ||
0.957499 | − | 0.288437i | \(-0.0931357\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.306788 | + | 0.177124i | −0.0178017 | + | 0.0102778i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.00000 | + | 1.73205i | −0.0578315 | + | 0.100167i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.35425 | − | 7.54178i | −0.250975 | − | 0.434701i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4.27579 | + | 2.46863i | 0.245638 | + | 0.141819i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.87451i | 0.106984i | 0.998568 | + | 0.0534919i | \(0.0170351\pi\) | ||||
−0.998568 | + | 0.0534919i | \(0.982965\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.0627461 | 0.00356950 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6.64575 | + | 11.5108i | 0.376846 | + | 0.652716i | 0.990601 | − | 0.136780i | \(-0.0436753\pi\) |
−0.613755 | + | 0.789496i | \(0.710342\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −16.7069 | − | 9.64575i | −0.944332 | − | 0.545210i | −0.0530161 | − | 0.998594i | \(-0.516883\pi\) |
−0.891316 | + | 0.453384i | \(0.850217\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 7.43310 | + | 4.29150i | 0.417485 | + | 0.241035i | 0.694000 | − | 0.719975i | \(-0.255847\pi\) |
−0.276516 | + | 0.961009i | \(0.589180\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.583005 | + | 1.00979i | 0.0326420 | + | 0.0565376i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 16.2288 | 0.905801 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.35425i | 0.130994i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 10.0312 | + | 5.79150i | 0.554725 | + | 0.320271i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 34.2288 | 1.88709 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.67712 | − | 2.90486i | 0.0921831 | − | 0.159666i | −0.816246 | − | 0.577704i | \(-0.803949\pi\) |
0.908429 | + | 0.418038i | \(0.137282\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.98450 | + | 1.14575i | −0.108750 | + | 0.0627868i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 19.2915i | 1.05088i | 0.850832 | + | 0.525438i | \(0.176098\pi\) | ||||
−0.850832 | + | 0.525438i | \(0.823902\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4.29150 | + | 7.43310i | 0.233082 | + | 0.403711i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.708497 | − | 1.22715i | 0.0383673 | − | 0.0664541i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.5203i | 1.00000i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 9.97684 | − | 5.76013i | 0.535585 | − | 0.309220i | −0.207703 | − | 0.978192i | \(-0.566599\pi\) |
0.743288 | + | 0.668972i | \(0.233265\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.70850 | −0.252040 | −0.126020 | − | 0.992028i | \(-0.540220\pi\) | ||||
−0.126020 | + | 0.992028i | \(0.540220\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −14.6681 | + | 8.46863i | −0.780704 | + | 0.450740i | −0.836680 | − | 0.547693i | \(-0.815506\pi\) |
0.0559759 | + | 0.998432i | \(0.482173\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 9.64575i | 0.510507i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −12.4686 | + | 21.5963i | −0.658069 | + | 1.13981i | 0.323046 | + | 0.946383i | \(0.395293\pi\) |
−0.981115 | + | 0.193426i | \(0.938040\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.29150 | + | 16.0934i | 0.489026 | + | 0.847019i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 10.8745i | 0.570764i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10.2836 | − | 5.93725i | 0.536801 | − | 0.309922i | −0.206981 | − | 0.978345i | \(-0.566364\pi\) |
0.743781 | + | 0.668423i | \(0.233030\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.82288 | + | 4.88936i | −0.146953 | + | 0.254530i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −10.1144 | + | 17.5186i | −0.525112 | + | 0.909521i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −20.4235 | − | 11.7915i | −1.05749 | − | 0.610541i | −0.132752 | − | 0.991149i | \(-0.542381\pi\) |
−0.924736 | + | 0.380608i | \(0.875715\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.29150i | 0.169521i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 15.3542 | 0.788695 | 0.394347 | − | 0.918961i | \(-0.370971\pi\) | ||||
0.394347 | + | 0.918961i | \(0.370971\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.677124 | − | 1.17281i | −0.0346901 | − | 0.0600851i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −8.04668 | − | 4.64575i | −0.411166 | − | 0.237387i | 0.280125 | − | 0.959964i | \(-0.409624\pi\) |
−0.691291 | + | 0.722577i | \(0.742958\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.85052 | + | 1.64575i | 0.144900 | + | 0.0836582i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −0.239870 | − | 0.415468i | −0.0121619 | − | 0.0210651i | 0.859880 | − | 0.510496i | \(-0.170538\pi\) |
−0.872042 | + | 0.489430i | \(0.837205\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.29150 | −0.368747 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 0.583005i | − | 0.0294087i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 17.7167 | + | 10.2288i | 0.889177 | + | 0.513367i | 0.873673 | − | 0.486513i | \(-0.161731\pi\) |
0.0155038 | + | 0.999880i | \(0.495065\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.854249 | − | 1.47960i | −0.0427659 | − | 0.0740728i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −17.7601 | + | 30.7614i | −0.886899 | + | 1.53615i | −0.0433765 | + | 0.999059i | \(0.513812\pi\) |
−0.843522 | + | 0.537095i | \(0.819522\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.46410 | − | 2.00000i | 0.172559 | − | 0.0996271i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 0.811762i | − | 0.0402375i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.79150 | + | 6.56708i | 0.187478 | + | 0.324721i | 0.944409 | − | 0.328774i | \(-0.106635\pi\) |
−0.756931 | + | 0.653495i | \(0.773302\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.645751 | − | 1.11847i | 0.0318526 | − | 0.0551703i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.14752 | + | 1.23987i | 0.105672 | + | 0.0610100i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 13.8021 | − | 7.96863i | 0.675890 | − | 0.390225i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −31.6458 | −1.54600 | −0.772998 | − | 0.634408i | \(-0.781244\pi\) | ||||
−0.772998 | + | 0.634408i | \(0.781244\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 28.8745 | 1.40726 | 0.703629 | − | 0.710568i | \(-0.251562\pi\) | ||||
0.703629 | + | 0.710568i | \(0.251562\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −11.2040 | + | 6.46863i | −0.544757 | + | 0.314515i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 30.6458i | 1.48305i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.177124 | − | 0.306788i | 0.00855164 | − | 0.0148119i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 13.9373 | + | 24.1400i | 0.671334 | + | 1.16278i | 0.977526 | + | 0.210815i | \(0.0676117\pi\) |
−0.306192 | + | 0.951970i | \(0.599055\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 3.29150i | − | 0.158180i | −0.996867 | − | 0.0790898i | \(-0.974799\pi\) | ||
0.996867 | − | 0.0790898i | \(-0.0252014\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.11847 | − | 0.645751i | 0.0535039 | − | 0.0308905i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −19.9059 | + | 34.4780i | −0.950056 | + | 1.64555i | −0.204759 | + | 0.978812i | \(0.565641\pi\) |
−0.745297 | + | 0.666733i | \(0.767692\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.50000 | − | 6.06218i | −0.166667 | − | 0.288675i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5.80973 | + | 3.35425i | 0.276029 | + | 0.159365i | 0.631624 | − | 0.775275i | \(-0.282389\pi\) |
−0.355596 | + | 0.934640i | \(0.615722\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4.93725i | 0.233524i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 32.1033 | 1.51505 | 0.757523 | − | 0.652808i | \(-0.226409\pi\) | ||||
0.757523 | + | 0.652808i | \(0.226409\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.00000 | − | 1.73205i | −0.0470882 | − | 0.0815591i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −9.83307 | − | 5.67712i | −0.461998 | − | 0.266735i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7.07197 | + | 4.08301i | 0.330813 | + | 0.190995i | 0.656202 | − | 0.754585i | \(-0.272162\pi\) |
−0.325389 | + | 0.945580i | \(0.605495\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.82288 | − | 3.15731i | −0.0850845 | − | 0.147371i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 10.7085 | 0.498744 | 0.249372 | − | 0.968408i | \(-0.419776\pi\) | ||||
0.249372 | + | 0.968408i | \(0.419776\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 33.9373i | 1.57720i | 0.614908 | + | 0.788599i | \(0.289193\pi\) | ||||
−0.614908 | + | 0.788599i | \(0.710807\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −19.6661 | − | 11.3542i | −0.910040 | − | 0.525412i | −0.0295961 | − | 0.999562i | \(-0.509422\pi\) |
−0.880444 | + | 0.474150i | \(0.842755\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 10.5000 | − | 18.1865i | 0.484845 | − | 0.839776i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 8.50000 | − | 14.7224i | 0.391659 | − | 0.678374i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.00979 | + | 0.583005i | −0.0464304 | + | 0.0268066i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 7.64575i | − | 0.350075i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 12.8229 | + | 22.2099i | 0.585892 | + | 1.01479i | 0.994764 | + | 0.102203i | \(0.0325891\pi\) |
−0.408871 | + | 0.912592i | \(0.634078\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.14575 | − | 1.98450i | 0.0522418 | − | 0.0904854i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4.58258 | − | 2.64575i | 0.208514 | − | 0.120386i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 35.0372 | − | 20.2288i | 1.58769 | − | 0.916652i | 0.594002 | − | 0.804464i | \(-0.297547\pi\) |
0.993687 | − | 0.112189i | \(-0.0357861\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −17.2288 | −0.779111 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −34.4575 | −1.55505 | −0.777523 | − | 0.628855i | \(-0.783524\pi\) | ||||
−0.777523 | + | 0.628855i | \(0.783524\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −10.3923 | + | 6.00000i | −0.468046 | + | 0.270226i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 16.7069 | − | 9.64575i | 0.749408 | − | 0.432671i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9.90588 | + | 17.1575i | −0.443448 | + | 0.768075i | −0.997943 | − | 0.0641127i | \(-0.979578\pi\) |
0.554495 | + | 0.832187i | \(0.312912\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 9.76013 | + | 16.9050i | 0.436050 | + | 0.755262i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 16.7085i | − | 0.744995i | −0.928033 | − | 0.372498i | \(-0.878502\pi\) | ||
0.928033 | − | 0.372498i | \(-0.121498\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −10.3923 | + | 6.00000i | −0.461538 | + | 0.266469i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −12.9373 | + | 22.4080i | −0.573434 | + | 0.993216i | 0.422776 | + | 0.906234i | \(0.361056\pi\) |
−0.996210 | + | 0.0869822i | \(0.972278\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.67712 | + | 9.83307i | −0.251141 | + | 0.434989i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.559237 | + | 0.322876i | 0.0246909 | + | 0.0142553i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 4.58301i | − | 0.201560i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 20.5830 | 0.903494 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.93725 | + | 13.7477i | 0.347737 | + | 0.602299i | 0.985847 | − | 0.167647i | \(-0.0536167\pi\) |
−0.638110 | + | 0.769945i | \(0.720283\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8.76893 | − | 5.06275i | −0.383439 | − | 0.221378i | 0.295875 | − | 0.955227i | \(-0.404389\pi\) |
−0.679313 | + | 0.733848i | \(0.737722\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 12.6293 | + | 7.29150i | 0.550139 | + | 0.317623i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9.50000 | − | 16.4545i | −0.413043 | − | 0.715412i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.937254 | −0.0406734 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 5.64575i | − | 0.244545i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 20.1710 | + | 11.6458i | 0.870444 | + | 0.502551i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.47974 | 0.106810 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −13.4373 | + | 23.2740i | −0.577713 | + | 1.00063i | 0.418028 | + | 0.908434i | \(0.362721\pi\) |
−0.995741 | + | 0.0921937i | \(0.970612\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −12.6293 | + | 7.29150i | −0.541973 | + | 0.312908i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 0.125492i | − | 0.00536566i | −0.999996 | − | 0.00268283i | \(-0.999146\pi\) | ||
0.999996 | − | 0.00268283i | \(-0.000853972\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −5.79150 | − | 10.0312i | −0.247175 | − | 0.428120i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.06275 | − | 1.84073i | 0.0452745 | − | 0.0784177i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 3.58301i | − | 0.152365i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 14.4700 | − | 8.35425i | 0.613113 | − | 0.353981i | −0.161070 | − | 0.986943i | \(-0.551494\pi\) |
0.774183 | + | 0.632962i | \(0.218161\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.29150 | −0.139216 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.29150 | 0.0545273 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 4.78068 | − | 2.76013i | 0.201482 | − | 0.116326i | −0.395865 | − | 0.918309i | \(-0.629555\pi\) |
0.597346 | + | 0.801983i | \(0.296222\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.29129 | + | 1.32288i | 0.0962250 | + | 0.0555556i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 2.46863 | − | 4.27579i | 0.103490 | − | 0.179250i | −0.809630 | − | 0.586940i | \(-0.800332\pi\) |
0.913120 | + | 0.407690i | \(0.133666\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.96863 | − | 5.14181i | −0.124233 | − | 0.215178i | 0.797200 | − | 0.603716i | \(-0.206314\pi\) |
−0.921433 | + | 0.388537i | \(0.872980\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 13.5203i | − | 0.564817i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.96900 | − | 2.29150i | 0.165232 | − | 0.0953965i | −0.415104 | − | 0.909774i | \(-0.636255\pi\) |
0.580335 | + | 0.814378i | \(0.302921\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −8.00000 | + | 13.8564i | −0.332469 | + | 0.575853i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.17712 | + | 3.77089i | 0.0903223 | + | 0.156443i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.34563 | + | 1.35425i | 0.0971460 | + | 0.0560872i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 6.00000i | − | 0.247647i | −0.992304 | − | 0.123823i | \(-0.960484\pi\) | ||
0.992304 | − | 0.123823i | \(-0.0395156\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.58301 | −0.106431 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −4.35425 | − | 7.54178i | −0.179110 | − | 0.310227i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −0.504897 | − | 0.291503i | −0.0207336 | − | 0.0119706i | 0.489597 | − | 0.871949i | \(-0.337144\pi\) |
−0.510331 | + | 0.859978i | \(0.670477\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −0.559237 | − | 0.322876i | −0.0228880 | − | 0.0132144i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −16.4686 | − | 28.5245i | −0.672890 | − | 1.16548i | −0.977081 | − | 0.212868i | \(-0.931719\pi\) |
0.304191 | − | 0.952611i | \(-0.401614\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 14.2915 | 0.582963 | 0.291481 | − | 0.956577i | \(-0.405852\pi\) | ||||
0.291481 | + | 0.956577i | \(0.405852\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 7.93725i | 0.323230i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −14.4156 | − | 8.32288i | −0.585113 | − | 0.337815i | 0.178050 | − | 0.984021i | \(-0.443021\pi\) |
−0.763163 | + | 0.646206i | \(0.776355\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 4.35425 | − | 7.54178i | 0.176443 | − | 0.305608i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.46863 | − | 11.2040i | 0.261693 | − | 0.453265i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 30.5633 | − | 17.6458i | 1.23444 | − | 0.712705i | 0.266489 | − | 0.963838i | \(-0.414136\pi\) |
0.967953 | + | 0.251133i | \(0.0808031\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 41.8745i | 1.68580i | 0.538067 | + | 0.842902i | \(0.319155\pi\) | ||||
−0.538067 | + | 0.842902i | \(0.680845\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 12.3542 | + | 21.3982i | 0.496559 | + | 0.860066i | 0.999992 | − | 0.00396857i | \(-0.00126324\pi\) |
−0.503433 | + | 0.864034i | \(0.667930\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.00000 | + | 1.73205i | −0.0401286 | + | 0.0695048i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 18.3542i | 0.735347i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.198109 | + | 0.114378i | −0.00791171 | + | 0.00456783i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 8.35425 | 0.333106 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.35425 | −0.0539118 | −0.0269559 | − | 0.999637i | \(-0.508581\pi\) | ||||
−0.0269559 | + | 0.999637i | \(0.508581\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.78639 | − | 1.03137i | 0.0710026 | − | 0.0409934i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.06218 | + | 3.50000i | 0.240192 | + | 0.138675i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3.64575 | + | 6.31463i | −0.144224 | + | 0.249803i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 27.3542i | − | 1.07875i | −0.842067 | − | 0.539373i | \(-0.818661\pi\) | ||
0.842067 | − | 0.539373i | \(-0.181339\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 43.8956 | − | 25.3431i | 1.72571 | − | 0.996341i | 0.820126 | − | 0.572183i | \(-0.193903\pi\) |
0.905588 | − | 0.424159i | \(-0.139430\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.166010 | − | 0.287539i | 0.00651648 | − | 0.0112869i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −10.5830 | −0.414781 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −14.0545 | − | 8.11438i | −0.549996 | − | 0.317540i | 0.199125 | − | 0.979974i | \(-0.436190\pi\) |
−0.749120 | + | 0.662434i | \(0.769523\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 4.29150i | − | 0.167427i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −40.1033 | −1.56220 | −0.781101 | − | 0.624405i | \(-0.785341\pi\) | ||||
−0.781101 | + | 0.624405i | \(0.785341\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −0.854249 | − | 1.47960i | −0.0332264 | − | 0.0575499i | 0.848934 | − | 0.528499i | \(-0.177245\pi\) |
−0.882160 | + | 0.470949i | \(0.843912\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.15731 | + | 1.82288i | 0.122620 | + | 0.0707946i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.70105 | + | 3.29150i | 0.220746 | + | 0.127447i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −6.96863 | − | 12.0700i | −0.269423 | − | 0.466654i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.10326 | 0.158405 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.29150i | 0.0883309i | 0.999024 | + | 0.0441655i | \(0.0140629\pi\) | ||||
−0.999024 | + | 0.0441655i | \(0.985937\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −33.5225 | − | 19.3542i | −1.28838 | − | 0.743844i | −0.310011 | − | 0.950733i | \(-0.600333\pi\) |
−0.978365 | + | 0.206889i | \(0.933666\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.90588 | + | 8.49723i | 0.188270 | + | 0.326094i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.35425 | + | 7.54178i | −0.166855 | + | 0.289002i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 17.4099 | − | 10.0516i | 0.666173 | − | 0.384615i | −0.128452 | − | 0.991716i | \(-0.541001\pi\) |
0.794625 | + | 0.607101i | \(0.207668\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 20.2915i | − | 0.774169i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.82288 | + | 6.62141i | 0.145640 | + | 0.252256i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.61438 | + | 13.1885i | −0.289665 | + | 0.501714i | −0.973730 | − | 0.227707i | \(-0.926877\pi\) |
0.684065 | + | 0.729421i | \(0.260210\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.811686 | + | 0.468627i | −0.0308334 | + | 0.0178017i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 17.8254 | − | 10.2915i | 0.675185 | − | 0.389818i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 24.2288 | 0.916416 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −25.0627 | −0.946607 | −0.473303 | − | 0.880899i | \(-0.656939\pi\) | ||||
−0.473303 | + | 0.880899i | \(0.656939\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.28149 | + | 0.739870i | −0.0483324 | + | 0.0279047i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 11.3127 | + | 6.53137i | 0.425457 | + | 0.245638i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.08301 | + | 5.33992i | −0.115785 | + | 0.200545i | −0.918093 | − | 0.396365i | \(-0.870272\pi\) |
0.802308 | + | 0.596910i | \(0.203605\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.677124 | + | 1.17281i | 0.0253941 | + | 0.0439840i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 8.00000i | − | 0.299602i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −8.15536 | + | 4.70850i | −0.304567 | + | 0.175842i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.11438 | − | 1.93016i | 0.0415593 | − | 0.0719828i | −0.844498 | − | 0.535559i | \(-0.820101\pi\) |
0.886057 | + | 0.463577i | \(0.153434\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.166010 | 0.00618255 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −0.252449 | − | 0.145751i | −0.00938867 | − | 0.00542055i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 27.1033i | − | 1.00520i | −0.864518 | − | 0.502602i | \(-0.832376\pi\) | ||
0.864518 | − | 0.502602i | \(-0.167624\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6.00000 | − | 10.3923i | −0.221918 | − | 0.384373i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −27.7479 | − | 16.0203i | −1.02489 | − | 0.591722i | −0.109375 | − | 0.994001i | \(-0.534885\pi\) |
−0.915517 | + | 0.402279i | \(0.868218\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2.43506 | − | 1.40588i | −0.0896965 | − | 0.0517863i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −25.2601 | − | 43.7518i | −0.929209 | − | 1.60944i | −0.784648 | − | 0.619941i | \(-0.787157\pi\) |
−0.144560 | − | 0.989496i | \(-0.546177\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.645751 | −0.0237223 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 11.4170i | − | 0.418849i | −0.977825 | − | 0.209424i | \(-0.932841\pi\) | ||
0.977825 | − | 0.209424i | \(-0.0671590\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.42526 | − | 0.822876i | −0.0521476 | − | 0.0301074i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 42.9373 | 1.56889 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 16.6771 | − | 28.8856i | 0.608557 | − | 1.05405i | −0.382922 | − | 0.923781i | \(-0.625082\pi\) |
0.991478 | − | 0.130271i | \(-0.0415846\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 24.9517 | − | 14.4059i | 0.909291 | − | 0.524979i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 11.0000i | − | 0.399802i | −0.979816 | − | 0.199901i | \(-0.935938\pi\) | ||
0.979816 | − | 0.199901i | \(-0.0640620\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.354249 | − | 0.613577i | −0.0128584 | − | 0.0222714i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 22.1771 | − | 38.4119i | 0.803920 | − | 1.39243i | −0.113098 | − | 0.993584i | \(-0.536077\pi\) |
0.917018 | − | 0.398847i | \(-0.130589\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 26.5400 | + | 15.3229i | 0.960812 | + | 0.554725i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.811686 | − | 0.468627i | 0.0293083 | − | 0.0169211i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4.00000 | −0.144244 | −0.0721218 | − | 0.997396i | \(-0.522977\pi\) | ||||
−0.0721218 | + | 0.997396i | \(0.522977\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 17.6458 | 0.635496 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −23.0216 | + | 13.2915i | −0.828028 | + | 0.478062i | −0.853177 | − | 0.521622i | \(-0.825327\pi\) |
0.0251491 | + | 0.999684i | \(0.491994\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −5.25049 | + | 3.03137i | −0.188360 | + | 0.108750i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.82288 | + | 3.15731i | −0.0653113 | + | 0.113122i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.29150 | − | 2.23695i | −0.0462136 | − | 0.0800443i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.29150i | 0.117629i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −38.9519 | + | 22.4889i | −1.38849 | + | 0.801642i | −0.993145 | − | 0.116892i | \(-0.962707\pi\) |
−0.395340 | + | 0.918535i | \(0.629373\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −12.0000 | + | 20.7846i | −0.427211 | + | 0.739952i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 11.3542 | + | 19.6661i | 0.403711 | + | 0.699247i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 10.0312 | + | 5.79150i | 0.356218 | + | 0.205662i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 3.87451i | 0.137242i | 0.997643 | + | 0.0686211i | \(0.0218599\pi\) | ||||
−0.997643 | + | 0.0686211i | \(0.978140\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 47.1660 | 1.66861 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.46863 | − | 6.00784i | −0.122558 | − | 0.212277i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.31658 | + | 0.760130i | 0.0464612 | + | 0.0268244i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −17.5186 | − | 10.1144i | −0.616685 | − | 0.356043i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −17.3542 | − | 30.0584i | −0.610143 | − | 1.05680i | −0.991216 | − | 0.132254i | \(-0.957779\pi\) |
0.381073 | − | 0.924545i | \(-0.375555\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −7.93725 | −0.278715 | −0.139357 | − | 0.990242i | \(-0.544504\pi\) | ||||
−0.139357 | + | 0.990242i | \(0.544504\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2.70850i | 0.0949912i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.84073 | + | 1.06275i | 0.0643990 | + | 0.0371808i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.64575 | −0.0924500 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8.69738 | − | 15.0643i | 0.303541 | − | 0.525748i | −0.673395 | − | 0.739283i | \(-0.735164\pi\) |
0.976935 | + | 0.213535i | \(0.0684978\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −14.3070 | + | 8.26013i | −0.498709 | + | 0.287930i | −0.728180 | − | 0.685385i | \(-0.759634\pi\) |
0.229471 | + | 0.973315i | \(0.426300\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 42.5830i | 1.48076i | 0.672191 | + | 0.740378i | \(0.265354\pi\) | ||||
−0.672191 | + | 0.740378i | \(0.734646\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −19.6660 | − | 34.0625i | −0.683029 | − | 1.18304i | −0.974052 | − | 0.226325i | \(-0.927329\pi\) |
0.291023 | − | 0.956716i | \(-0.406004\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −12.5000 | + | 21.6506i | −0.433620 | + | 0.751052i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 25.5203i | 0.884225i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.46410 | − | 2.00000i | 0.119737 | − | 0.0691301i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −19.1660 | −0.661684 | −0.330842 | − | 0.943686i | \(-0.607333\pi\) | ||||
−0.330842 | + | 0.943686i | \(0.607333\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18.1660 | −0.626414 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 19.2507 | − | 11.1144i | 0.663028 | − | 0.382800i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 28.7712i | 0.988592i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 3.26013 | − | 5.64671i | 0.111887 | − | 0.193795i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.29150 | − | 3.96900i | −0.0785517 | − | 0.136056i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 2.00000i | − | 0.0684787i | −0.999414 | − | 0.0342393i | \(-0.989099\pi\) | ||
0.999414 | − | 0.0342393i | \(-0.0109009\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −23.5265 | + | 13.5830i | −0.803648 | + | 0.463987i | −0.844745 | − | 0.535169i | \(-0.820248\pi\) |
0.0410969 | + | 0.999155i | \(0.486915\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −20.5830 | + | 35.6508i | −0.702283 | + | 1.21639i | 0.265380 | + | 0.964144i | \(0.414503\pi\) |
−0.967663 | + | 0.252246i | \(0.918831\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −7.46863 | + | 12.9360i | −0.254530 | + | 0.440859i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 5.28558 | + | 3.05163i | 0.179923 | + | 0.103879i | 0.587257 | − | 0.809401i | \(-0.300208\pi\) |
−0.407333 | + | 0.913280i | \(0.633541\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 3.70850i | − | 0.125947i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.479741 | −0.0162741 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.96863 | − | 6.87386i | −0.134472 | − | 0.232912i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −3.21165 | − | 1.85425i | −0.108698 | − | 0.0627568i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −38.7538 | − | 22.3745i | −1.30862 | − | 0.755533i | −0.326756 | − | 0.945109i | \(-0.605956\pi\) |
−0.981866 | + | 0.189575i | \(0.939289\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 4.93725 | + | 8.55157i | 0.166529 | + | 0.288437i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 44.7085 | 1.50627 | 0.753134 | − | 0.657867i | \(-0.228541\pi\) | ||||
0.753134 | + | 0.657867i | \(0.228541\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 23.3542i | 0.785933i | 0.919553 | + | 0.392967i | \(0.128551\pi\) | ||||
−0.919553 | + | 0.392967i | \(0.871449\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −35.7595 | − | 20.6458i | −1.20069 | − | 0.693216i | −0.239978 | − | 0.970778i | \(-0.577140\pi\) |
−0.960708 | + | 0.277562i | \(0.910474\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.79150 | − | 3.10297i | −0.0600851 | − | 0.104070i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.177124 | − | 0.306788i | 0.00593389 | − | 0.0102778i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −7.23499 | + | 4.17712i | −0.242110 | + | 0.139782i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 2.00000i | − | 0.0667781i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −6.58301 | − | 11.4021i | −0.219556 | − | 0.380281i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −13.9373 | + | 24.1400i | −0.464317 | + | 0.804221i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 7.54178 | + | 4.35425i | 0.250975 | + | 0.144900i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −26.8275 | + | 15.4889i | −0.890794 | + | 0.514300i | −0.874202 | − | 0.485562i | \(-0.838615\pi\) |
−0.0165917 | + | 0.999862i | \(0.505282\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −4.93725 | −0.163758 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 32.3320 | 1.07121 | 0.535604 | − | 0.844469i | \(-0.320084\pi\) | ||||
0.535604 | + | 0.844469i | \(0.320084\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.504897 | − | 0.291503i | 0.0167097 | − | 0.00964733i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 1.54249i | − | 0.0509374i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 24.4575 | − | 42.3617i | 0.806779 | − | 1.39738i | −0.108305 | − | 0.994118i | \(-0.534542\pi\) |
0.915084 | − | 0.403264i | \(-0.132124\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −0.937254 | − | 1.62337i | −0.0308836 | − | 0.0534919i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 7.29150i | − | 0.240003i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −0.0543397 | + | 0.0313730i | −0.00178475 | + | 0.00103043i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.17712 | − | 2.03884i | 0.0386202 | − | 0.0668921i | −0.846069 | − | 0.533073i | \(-0.821037\pi\) |
0.884689 | + | 0.466181i | \(0.154370\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.26013 | − | 3.91466i | −0.0740728 | − | 0.128298i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −11.5108 | − | 6.64575i | −0.376846 | − | 0.217572i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 19.2915 | 0.629554 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −6.87451 | − | 11.9070i | −0.224103 | − | 0.388157i | 0.731947 | − | 0.681361i | \(-0.238612\pi\) |
−0.956050 | + | 0.293204i | \(0.905278\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −9.77873 | − | 5.64575i | −0.318439 | − | 0.183851i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 23.1302 | + | 13.3542i | 0.751632 | + | 0.433955i | 0.826283 | − | 0.563255i | \(-0.190451\pi\) |
−0.0746515 | + | 0.997210i | \(0.523784\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.14575 | + | 3.71655i | 0.0696540 | + | 0.120644i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −8.58301 | −0.278323 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 47.5203i | 1.53933i | 0.638447 | + | 0.769666i | \(0.279577\pi\) | ||||
−0.638447 | + | 0.769666i | \(0.720423\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.00979 | − | 0.583005i | −0.0326420 | − | 0.0188459i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.70850 | − | 2.95920i | 0.0551703 | − | 0.0955577i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.50000 | − | 12.9904i | 0.241935 | − | 0.419045i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −14.0545 | + | 8.11438i | −0.452900 | + | 0.261482i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 29.9373i | − | 0.962717i | −0.876524 | − | 0.481359i | \(-0.840143\pi\) | ||
0.876524 | − | 0.481359i | \(-0.159857\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.17712 | − | 2.03884i | −0.0378147 | − | 0.0654970i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 26.2804 | − | 45.5190i | 0.843378 | − | 1.46077i | −0.0436447 | − | 0.999047i | \(-0.513897\pi\) |
0.887023 | − | 0.461726i | \(-0.152770\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 36.5168 | − | 21.0830i | 1.17068 | − | 0.675890i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −21.3789 | + | 12.3431i | −0.683973 | + | 0.394892i | −0.801350 | − | 0.598196i | \(-0.795885\pi\) |
0.117377 | + | 0.993087i | \(0.462551\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.45751 | 0.0785425 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −11.5830 | −0.369817 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −4.88936 | + | 2.82288i | −0.155946 | + | 0.0900358i | −0.575943 | − | 0.817490i | \(-0.695365\pi\) |
0.419996 | + | 0.907526i | \(0.362031\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −29.6430 | + | 17.1144i | −0.943546 | + | 0.544757i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.29150 | + | 5.70105i | −0.104664 | + | 0.181283i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 11.9373 | + | 20.6759i | 0.379199 | + | 0.656793i | 0.990946 | − | 0.134261i | \(-0.0428661\pi\) |
−0.611747 | + | 0.791054i | \(0.709533\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 3.35425i | 0.106444i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −42.2179 | + | 24.3745i | −1.33705 | + | 0.771948i | −0.986370 | − | 0.164545i | \(-0.947384\pi\) |
−0.350684 | + | 0.936494i | \(0.614051\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.14575 | − | 1.98450i | 0.0362500 | − | 0.0627868i |
(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.h.1549.1 | 8 | ||
5.2 | odd | 4 | 2100.2.q.i.1801.1 | yes | 4 | ||
5.3 | odd | 4 | 2100.2.q.g.1801.2 | yes | 4 | ||
5.4 | even | 2 | inner | 2100.2.bc.h.1549.4 | 8 | ||
7.4 | even | 3 | inner | 2100.2.bc.h.949.4 | 8 | ||
35.4 | even | 6 | inner | 2100.2.bc.h.949.1 | 8 | ||
35.18 | odd | 12 | 2100.2.q.g.1201.2 | ✓ | 4 | ||
35.32 | odd | 12 | 2100.2.q.i.1201.1 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2100.2.q.g.1201.2 | ✓ | 4 | 35.18 | odd | 12 | ||
2100.2.q.g.1801.2 | yes | 4 | 5.3 | odd | 4 | ||
2100.2.q.i.1201.1 | yes | 4 | 35.32 | odd | 12 | ||
2100.2.q.i.1801.1 | yes | 4 | 5.2 | odd | 4 | ||
2100.2.bc.h.949.1 | 8 | 35.4 | even | 6 | inner | ||
2100.2.bc.h.949.4 | 8 | 7.4 | even | 3 | inner | ||
2100.2.bc.h.1549.1 | 8 | 1.1 | even | 1 | trivial | ||
2100.2.bc.h.1549.4 | 8 | 5.4 | even | 2 | inner |