Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [260,2,Mod(23,260)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(260, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([6, 9, 10]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("260.23");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 260 = 2^{2} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 260.bg (of order \(12\), degree \(4\), 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: | \(2.07611045255\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
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: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{12}]$ |
Embedding invariants
Embedding label | 147.1 | ||
Root | \(0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 260.147 |
Dual form | 260.2.bg.a.23.1 |
$q$-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 \(\left(\mathbb{Z}/260\mathbb{Z}\right)^\times\).
\(n\) | \(41\) | \(131\) | \(157\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.366025 | + | 1.36603i | 0.258819 | + | 0.965926i | ||||
\(3\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(4\) | −1.73205 | + | 1.00000i | −0.866025 | + | 0.500000i | ||||
\(5\) | 0.133975 | + | 2.23205i | 0.0599153 | + | 0.998203i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(8\) | −2.00000 | − | 2.00000i | −0.707107 | − | 0.707107i | ||||
\(9\) | −2.59808 | + | 1.50000i | −0.866025 | + | 0.500000i | ||||
\(10\) | −3.00000 | + | 1.00000i | −0.948683 | + | 0.316228i | ||||
\(11\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.59808 | + | 3.23205i | 0.443227 | + | 0.896410i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.00000 | − | 3.46410i | 0.500000 | − | 0.866025i | ||||
\(17\) | 0.0358984 | − | 0.133975i | 0.00870664 | − | 0.0324936i | −0.961436 | − | 0.275029i | \(-0.911312\pi\) |
0.970143 | + | 0.242536i | \(0.0779791\pi\) | |||||||
\(18\) | −3.00000 | − | 3.00000i | −0.707107 | − | 0.707107i | ||||
\(19\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(20\) | −2.46410 | − | 3.73205i | −0.550990 | − | 0.834512i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.96410 | + | 0.598076i | −0.992820 | + | 0.119615i | ||||
\(26\) | −3.83013 | + | 3.36603i | −0.751150 | + | 0.660132i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 9.23205 | + | 5.33013i | 1.71435 | + | 0.989780i | 0.928477 | + | 0.371391i | \(0.121119\pi\) |
0.785872 | + | 0.618389i | \(0.212214\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(32\) | 5.46410 | + | 1.46410i | 0.965926 | + | 0.258819i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.196152 | 0.0336399 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3.00000 | − | 5.19615i | 0.500000 | − | 0.866025i | ||||
\(37\) | −2.86603 | − | 10.6962i | −0.471172 | − | 1.75844i | −0.635571 | − | 0.772043i | \(-0.719235\pi\) |
0.164399 | − | 0.986394i | \(-0.447432\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 4.19615 | − | 4.73205i | 0.663470 | − | 0.748203i | ||||
\(41\) | 10.3301 | + | 5.96410i | 1.61329 | + | 0.931436i | 0.988600 | + | 0.150567i | \(0.0481100\pi\) |
0.624695 | + | 0.780869i | \(0.285223\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.69615 | − | 5.59808i | −0.550990 | − | 0.834512i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.06218 | + | 3.50000i | 0.866025 | + | 0.500000i | ||||
\(50\) | −2.63397 | − | 6.56218i | −0.372500 | − | 0.928032i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −6.00000 | − | 4.00000i | −0.832050 | − | 0.554700i | ||||
\(53\) | 5.29423 | − | 5.29423i | 0.727218 | − | 0.727218i | −0.242846 | − | 0.970065i | \(-0.578081\pi\) |
0.970065 | + | 0.242846i | \(0.0780811\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −3.90192 | + | 14.5622i | −0.512348 | + | 1.91211i | ||||
\(59\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.33013 | + | 2.30385i | 0.170305 | + | 0.294977i | 0.938527 | − | 0.345207i | \(-0.112191\pi\) |
−0.768221 | + | 0.640184i | \(0.778858\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.00000i | 1.00000i | ||||||||
\(65\) | −7.00000 | + | 4.00000i | −0.868243 | + | 0.496139i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(68\) | 0.0717968 | + | 0.267949i | 0.00870664 | + | 0.0324936i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(72\) | 8.19615 | + | 2.19615i | 0.965926 | + | 0.258819i | ||||
\(73\) | −1.16987 | − | 1.16987i | −0.136923 | − | 0.136923i | 0.635323 | − | 0.772246i | \(-0.280867\pi\) |
−0.772246 | + | 0.635323i | \(0.780867\pi\) | |||||||
\(74\) | 13.5622 | − | 7.83013i | 1.57657 | − | 0.910234i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(80\) | 8.00000 | + | 4.00000i | 0.894427 | + | 0.447214i | ||||
\(81\) | 4.50000 | − | 7.79423i | 0.500000 | − | 0.866025i | ||||
\(82\) | −4.36603 | + | 16.2942i | −0.482147 | + | 1.79940i | ||||
\(83\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.303848 | + | 0.0621778i | 0.0329569 | + | 0.00674413i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.00000 | + | 8.66025i | −0.529999 | + | 0.917985i | 0.469389 | + | 0.882992i | \(0.344474\pi\) |
−0.999388 | + | 0.0349934i | \(0.988859\pi\) | |||||||
\(90\) | 6.29423 | − | 7.09808i | 0.663470 | − | 0.748203i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −17.7583 | − | 4.75833i | −1.80309 | − | 0.483135i | −0.808632 | − | 0.588315i | \(-0.799792\pi\) |
−0.994453 | + | 0.105180i | \(0.966458\pi\) | |||||||
\(98\) | −2.56218 | + | 9.56218i | −0.258819 | + | 0.965926i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 8.00000 | − | 6.00000i | 0.800000 | − | 0.600000i | ||||
\(101\) | 9.16025 | − | 15.8660i | 0.911479 | − | 1.57873i | 0.0995037 | − | 0.995037i | \(-0.468274\pi\) |
0.811976 | − | 0.583691i | \(-0.198392\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(104\) | 3.26795 | − | 9.66025i | 0.320449 | − | 0.947266i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 9.16987 | + | 5.29423i | 0.890657 | + | 0.514221i | ||||
\(107\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −20.0000 | −1.91565 | −0.957826 | − | 0.287348i | \(-0.907226\pi\) | ||||
−0.957826 | + | 0.287348i | \(0.907226\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.06218 | − | 2.42820i | −0.852498 | − | 0.228426i | −0.193993 | − | 0.981003i | \(-0.562144\pi\) |
−0.658505 | + | 0.752577i | \(0.728811\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −21.3205 | −1.97956 | ||||||||
\(117\) | −9.00000 | − | 6.00000i | −0.832050 | − | 0.554700i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.50000 | + | 9.52628i | 0.500000 | + | 0.866025i | ||||
\(122\) | −2.66025 | + | 2.66025i | −0.240848 | + | 0.240848i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −2.00000 | − | 11.0000i | −0.178885 | − | 0.983870i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(128\) | −10.9282 | + | 2.92820i | −0.965926 | + | 0.258819i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −8.02628 | − | 8.09808i | −0.703951 | − | 0.710248i | ||||
\(131\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.339746 | + | 0.196152i | −0.0291330 | + | 0.0168199i | ||||
\(137\) | 12.9641 | + | 3.47372i | 1.10760 | + | 0.296780i | 0.765855 | − | 0.643013i | \(-0.222316\pi\) |
0.341743 | + | 0.939793i | \(0.388983\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 12.0000i | 1.00000i | ||||||||
\(145\) | −10.6603 | + | 21.3205i | −0.885286 | + | 1.77057i | ||||
\(146\) | 1.16987 | − | 2.02628i | 0.0968194 | − | 0.167696i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 15.6603 | + | 15.6603i | 1.28726 | + | 1.28726i | ||||
\(149\) | −11.0622 | − | 19.1603i | −0.906249 | − | 1.56967i | −0.819232 | − | 0.573462i | \(-0.805600\pi\) |
−0.0870170 | − | 0.996207i | \(-0.527733\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.107695 | + | 0.401924i | 0.00870664 | + | 0.0324936i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −17.2224 | − | 17.2224i | −1.37450 | − | 1.37450i | −0.853646 | − | 0.520854i | \(-0.825614\pi\) |
−0.520854 | − | 0.853646i | \(-0.674386\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2.53590 | + | 12.3923i | −0.200480 | + | 0.979698i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 12.2942 | + | 3.29423i | 0.965926 | + | 0.258819i | ||||
\(163\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(164\) | −23.8564 | −1.86287 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.89230 | + | 10.3301i | −0.607100 | + | 0.794625i | ||||
\(170\) | 0.0262794 | + | 0.437822i | 0.00201554 | + | 0.0335794i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 20.4904 | + | 5.49038i | 1.55785 | + | 0.417426i | 0.931984 | − | 0.362500i | \(-0.118077\pi\) |
0.625871 | + | 0.779926i | \(0.284744\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −13.6603 | − | 3.66025i | −1.02388 | − | 0.274348i | ||||
\(179\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(180\) | 12.0000 | + | 6.00000i | 0.894427 | + | 0.447214i | ||||
\(181\) | 8.32051 | 0.618458 | 0.309229 | − | 0.950988i | \(-0.399929\pi\) | ||||
0.309229 | + | 0.950988i | \(0.399929\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 23.4904 | − | 7.83013i | 1.72705 | − | 0.575682i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.06218 | − | 1.89230i | 0.508347 | − | 0.136211i | 0.00447566 | − | 0.999990i | \(-0.498575\pi\) |
0.503871 | + | 0.863779i | \(0.331909\pi\) | |||||||
\(194\) | − | 26.0000i | − | 1.86669i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −14.0000 | −1.00000 | ||||||||
\(197\) | 4.75833 | + | 17.7583i | 0.339017 | + | 1.26523i | 0.899448 | + | 0.437028i | \(0.143969\pi\) |
−0.560431 | + | 0.828201i | \(0.689365\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(200\) | 11.1244 | + | 8.73205i | 0.786611 | + | 0.617449i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 25.0263 | + | 6.70577i | 1.76084 | + | 0.471816i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −11.9282 | + | 23.8564i | −0.833102 | + | 1.66620i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 14.3923 | + | 0.928203i | 0.997927 | + | 0.0643593i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(212\) | −3.87564 | + | 14.4641i | −0.266180 | + | 0.993399i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −7.32051 | − | 27.3205i | −0.495807 | − | 1.85038i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.490381 | − | 0.0980762i | 0.0329866 | − | 0.00659732i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 12.0000 | − | 9.00000i | 0.800000 | − | 0.600000i | ||||
\(226\) | − | 13.2679i | − | 0.882571i | ||||||
\(227\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 30.0000 | 1.98246 | 0.991228 | − | 0.132164i | \(-0.0421925\pi\) | ||||
0.991228 | + | 0.132164i | \(0.0421925\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −7.80385 | − | 29.1244i | −0.512348 | − | 1.91211i | ||||
\(233\) | −5.00000 | + | 5.00000i | −0.327561 | + | 0.327561i | −0.851658 | − | 0.524097i | \(-0.824403\pi\) |
0.524097 | + | 0.851658i | \(0.324403\pi\) | |||||||
\(234\) | 4.90192 | − | 14.4904i | 0.320449 | − | 0.947266i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −18.9904 | + | 10.9641i | −1.22328 | + | 0.706260i | −0.965615 | − | 0.259975i | \(-0.916286\pi\) |
−0.257663 | + | 0.966235i | \(0.582952\pi\) | |||||||
\(242\) | −11.0000 | + | 11.0000i | −0.707107 | + | 0.707107i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −4.60770 | − | 2.66025i | −0.294977 | − | 0.170305i | ||||
\(245\) | −7.00000 | + | 14.0000i | −0.447214 | + | 0.894427i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 14.2942 | − | 6.75833i | 0.904046 | − | 0.427434i | ||||
\(251\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.00000 | − | 13.8564i | −0.500000 | − | 0.866025i | ||||
\(257\) | 30.3564 | − | 8.13397i | 1.89358 | − | 0.507383i | 0.895528 | − | 0.445005i | \(-0.146798\pi\) |
0.998053 | − | 0.0623783i | \(-0.0198685\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 8.12436 | − | 13.9282i | 0.503851 | − | 0.863790i | ||||
\(261\) | −31.9808 | −1.97956 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 12.5263 | + | 11.1077i | 0.769483 | + | 0.682340i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 22.5167 | − | 13.0000i | 1.37287 | − | 0.792624i | 0.381577 | − | 0.924337i | \(-0.375381\pi\) |
0.991288 | + | 0.131713i | \(0.0420477\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(272\) | −0.392305 | − | 0.392305i | −0.0237870 | − | 0.0237870i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 18.9808i | 1.14667i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.20577 | − | 30.6244i | 0.493037 | − | 1.84004i | −0.0477206 | − | 0.998861i | \(-0.515196\pi\) |
0.540758 | − | 0.841178i | \(-0.318138\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 22.7128i | 1.35493i | 0.735554 | + | 0.677466i | \(0.236922\pi\) | ||||
−0.735554 | + | 0.677466i | \(0.763078\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −16.3923 | + | 4.39230i | −0.965926 | + | 0.258819i | ||||
\(289\) | 14.7058 | + | 8.49038i | 0.865045 | + | 0.499434i | ||||
\(290\) | −33.0263 | − | 6.75833i | −1.93937 | − | 0.396863i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 3.19615 | + | 0.856406i | 0.187041 | + | 0.0501174i | ||||
\(293\) | 8.23205 | − | 30.7224i | 0.480922 | − | 1.79482i | −0.116841 | − | 0.993151i | \(-0.537277\pi\) |
0.597763 | − | 0.801673i | \(-0.296056\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −15.6603 | + | 27.1244i | −0.910234 | + | 1.57657i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 22.1244 | − | 22.1244i | 1.28163 | − | 1.28163i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4.96410 | + | 3.27757i | −0.284244 | + | 0.187673i | ||||
\(306\) | −0.509619 | + | 0.294229i | −0.0291330 | + | 0.0168199i | ||||
\(307\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 25.0000 | − | 25.0000i | 1.41308 | − | 1.41308i | 0.678280 | − | 0.734803i | \(-0.262726\pi\) |
0.734803 | − | 0.678280i | \(-0.237274\pi\) | |||||||
\(314\) | 17.2224 | − | 29.8301i | 0.971918 | − | 1.68341i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −20.1506 | + | 20.1506i | −1.13177 | + | 1.13177i | −0.141890 | + | 0.989882i | \(0.545318\pi\) |
−0.989882 | + | 0.141890i | \(0.954682\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −17.8564 | + | 1.07180i | −0.998203 | + | 0.0599153i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 18.0000i | 1.00000i | ||||||||
\(325\) | −9.86603 | − | 15.0885i | −0.547269 | − | 0.836957i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −8.73205 | − | 32.5885i | −0.482147 | − | 1.79940i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 23.4904 | + | 23.4904i | 1.28726 | + | 1.28726i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 18.5622 | + | 18.5622i | 1.01115 | + | 1.01115i | 0.999937 | + | 0.0112091i | \(0.00356804\pi\) |
0.0112091 | + | 0.999937i | \(0.496432\pi\) | |||||||
\(338\) | −17.0000 | − | 7.00000i | −0.924678 | − | 0.380750i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −0.588457 | + | 0.196152i | −0.0319136 | + | 0.0106379i | ||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 30.0000i | 1.61281i | ||||||||
\(347\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.00000 | − | 8.66025i | 0.267644 | − | 0.463573i | −0.700609 | − | 0.713545i | \(-0.747088\pi\) |
0.968253 | + | 0.249973i | \(0.0804216\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −35.7224 | + | 9.57180i | −1.90131 | + | 0.509455i | −0.904819 | + | 0.425797i | \(0.859994\pi\) |
−0.996495 | + | 0.0836583i | \(0.973340\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 20.0000i | − | 1.06000i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(360\) | −3.80385 | + | 18.5885i | −0.200480 | + | 0.979698i | ||||
\(361\) | −9.50000 | + | 16.4545i | −0.500000 | + | 0.866025i | ||||
\(362\) | 3.04552 | + | 11.3660i | 0.160069 | + | 0.597385i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.45448 | − | 2.76795i | 0.128473 | − | 0.144881i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −35.7846 | −1.86287 | ||||||||
\(370\) | 19.2942 | + | 29.2224i | 1.00306 | + | 1.51920i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −30.0885 | − | 8.06218i | −1.55792 | − | 0.417444i | −0.625917 | − | 0.779890i | \(-0.715275\pi\) |
−0.932005 | + | 0.362446i | \(0.881942\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.47372 | + | 38.3564i | −0.127403 | + | 1.97546i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 5.16987 | + | 8.95448i | 0.263140 | + | 0.455771i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 35.5167 | − | 9.51666i | 1.80309 | − | 0.483135i | ||||
\(389\) | 34.3205i | 1.74012i | 0.492947 | + | 0.870059i | \(0.335920\pi\) | ||||
−0.492947 | + | 0.870059i | \(0.664080\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −5.12436 | − | 19.1244i | −0.258819 | − | 0.965926i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −22.5167 | + | 13.0000i | −1.13437 | + | 0.654931i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 17.7583 | + | 4.75833i | 0.891265 | + | 0.238814i | 0.675261 | − | 0.737579i | \(-0.264031\pi\) |
0.216004 | + | 0.976392i | \(0.430698\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −7.85641 | + | 18.3923i | −0.392820 | + | 0.919615i | ||||
\(401\) | −18.8205 | − | 10.8660i | −0.939851 | − | 0.542623i | −0.0499376 | − | 0.998752i | \(-0.515902\pi\) |
−0.889914 | + | 0.456129i | \(0.849236\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 36.6410i | 1.82296i | ||||||||
\(405\) | 18.0000 | + | 9.00000i | 0.894427 | + | 0.447214i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −12.5981 | − | 21.8205i | −0.622935 | − | 1.07895i | −0.988936 | − | 0.148340i | \(-0.952607\pi\) |
0.366002 | − | 0.930614i | \(-0.380726\pi\) | |||||||
\(410\) | −36.9545 | − | 7.56218i | −1.82505 | − | 0.373469i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 4.00000 | + | 20.0000i | 0.196116 | + | 0.980581i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 9.24871i | − | 0.450755i | −0.974272 | − | 0.225377i | \(-0.927639\pi\) | ||
0.974272 | − | 0.225377i | \(-0.0723615\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −21.1769 | −1.02844 | ||||||||
\(425\) | −0.0980762 | + | 0.686533i | −0.00475740 | + | 0.0333018i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −30.8923 | − | 8.27757i | −1.48459 | − | 0.397795i | −0.576683 | − | 0.816968i | \(-0.695653\pi\) |
−0.907906 | + | 0.419173i | \(0.862320\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 34.6410 | − | 20.0000i | 1.65900 | − | 0.957826i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −21.0000 | −1.00000 | ||||||||
\(442\) | 0.313467 | + | 0.633975i | 0.0149101 | + | 0.0301551i | ||||
\(443\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −20.0000 | − | 10.0000i | −0.948091 | − | 0.474045i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −20.0000 | − | 34.6410i | −0.943858 | − | 1.63481i | −0.758021 | − | 0.652230i | \(-0.773834\pi\) |
−0.185837 | − | 0.982581i | \(-0.559500\pi\) | |||||||
\(450\) | 16.6865 | + | 13.0981i | 0.786611 | + | 0.617449i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 18.1244 | − | 4.85641i | 0.852498 | − | 0.228426i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.81347 | − | 17.9641i | −0.225164 | − | 0.840325i | −0.982339 | − | 0.187112i | \(-0.940087\pi\) |
0.757174 | − | 0.653213i | \(-0.226579\pi\) | |||||||
\(458\) | 10.9808 | + | 40.9808i | 0.513097 | + | 1.91491i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 19.8397 | − | 11.4545i | 0.924029 | − | 0.533488i | 0.0391109 | − | 0.999235i | \(-0.487547\pi\) |
0.884918 | + | 0.465746i | \(0.154214\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(464\) | 36.9282 | − | 21.3205i | 1.71435 | − | 0.989780i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −8.66025 | − | 5.00000i | −0.401179 | − | 0.231621i | ||||
\(467\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(468\) | 21.5885 | + | 1.39230i | 0.997927 | + | 0.0643593i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5.81347 | + | 21.6962i | −0.266180 | + | 0.993399i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 29.9904 | − | 26.3564i | 1.36744 | − | 1.20175i | ||||
\(482\) | −21.9282 | − | 21.9282i | −0.998802 | − | 0.998802i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −19.0526 | − | 11.0000i | −0.866025 | − | 0.500000i | ||||
\(485\) | 8.24167 | − | 40.2750i | 0.374235 | − | 1.82879i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(488\) | 1.94744 | − | 7.26795i | 0.0881565 | − | 0.329005i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −21.6865 | − | 4.43782i | −0.979698 | − | 0.200480i | ||||
\(491\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.04552 | − | 1.04552i | 0.0470877 | − | 0.0470877i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(500\) | 14.4641 | + | 17.0526i | 0.646854 | + | 0.762614i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 36.6410 | + | 18.3205i | 1.63050 | + | 0.815252i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 16.5526 | − | 28.6699i | 0.733679 | − | 1.27077i | −0.221621 | − | 0.975133i | \(-0.571135\pi\) |
0.955300 | − | 0.295637i | \(-0.0955319\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 16.0000 | − | 16.0000i | 0.707107 | − | 0.707107i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 22.2224 | + | 38.4904i | 0.980189 | + | 1.69774i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 22.0000 | + | 6.00000i | 0.964764 | + | 0.263117i | ||||
\(521\) | −23.6410 | −1.03573 | −0.517866 | − | 0.855462i | \(-0.673273\pi\) | ||||
−0.517866 | + | 0.855462i | \(0.673273\pi\) | |||||||
\(522\) | −11.7058 | − | 43.6865i | −0.512348 | − | 1.91211i | ||||
\(523\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −19.9186 | + | 11.5000i | −0.866025 | + | 0.500000i | ||||
\(530\) | −10.5885 | + | 21.1769i | −0.459933 | + | 0.919866i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.76795 | + | 42.9186i | −0.119893 | + | 1.85901i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 26.0000 | + | 26.0000i | 1.12094 | + | 1.12094i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 46.3731i | − | 1.99373i | −0.0790969 | − | 0.996867i | \(-0.525204\pi\) | ||
0.0790969 | − | 0.996867i | \(-0.474796\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0.392305 | − | 0.679492i | 0.0168199 | − | 0.0291330i | ||||
\(545\) | −2.67949 | − | 44.6410i | −0.114777 | − | 1.91221i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(548\) | −25.9282 | + | 6.94744i | −1.10760 | + | 0.296780i | ||||
\(549\) | −6.91154 | − | 3.99038i | −0.294977 | − | 0.170305i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 44.8372 | 1.90495 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 7.62436 | + | 28.4545i | 0.323054 | + | 1.20566i | 0.916253 | + | 0.400599i | \(0.131198\pi\) |
−0.593199 | + | 0.805056i | \(0.702135\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −31.0263 | + | 8.31347i | −1.30876 | + | 0.350682i | ||||
\(563\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.20577 | − | 20.5526i | 0.176938 | − | 0.864653i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 22.5167 | + | 13.0000i | 0.943948 | + | 0.544988i | 0.891196 | − | 0.453619i | \(-0.149867\pi\) |
0.0527519 | + | 0.998608i | \(0.483201\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −12.0000 | − | 20.7846i | −0.500000 | − | 0.866025i | ||||
\(577\) | 33.1506 | − | 33.1506i | 1.38008 | − | 1.38008i | 0.535620 | − | 0.844459i | \(-0.320078\pi\) |
0.844459 | − | 0.535620i | \(-0.179922\pi\) | |||||||
\(578\) | −6.21539 | + | 23.1962i | −0.258526 | + | 0.964833i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −2.85641 | − | 47.5885i | −0.118606 | − | 1.97600i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 4.67949i | 0.193639i | ||||||||
\(585\) | 12.1865 | − | 20.8923i | 0.503851 | − | 0.863790i | ||||
\(586\) | 44.9808 | 1.85814 | ||||||||
\(587\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −42.7846 | − | 11.4641i | −1.75844 | − | 0.471172i | ||||
\(593\) | 2.50962 | + | 2.50962i | 0.103058 | + | 0.103058i | 0.756756 | − | 0.653698i | \(-0.226783\pi\) |
−0.653698 | + | 0.756756i | \(0.726783\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 38.3205 | + | 22.1244i | 1.56967 | + | 0.906249i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.66987 | + | 13.2846i | −0.312861 | + | 0.541891i | −0.978980 | − | 0.203954i | \(-0.934621\pi\) |
0.666120 | + | 0.745845i | \(0.267954\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −20.5263 | + | 13.5526i | −0.834512 | + | 0.550990i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −6.29423 | − | 5.58142i | −0.254846 | − | 0.225985i | ||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −0.588457 | − | 0.588457i | −0.0237870 | − | 0.0237870i | ||||
\(613\) | −42.0885 | + | 11.2776i | −1.69994 | + | 0.455497i | −0.972924 | − | 0.231127i | \(-0.925759\pi\) |
−0.727013 | + | 0.686624i | \(0.759092\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −39.3564 | − | 10.5455i | −1.58443 | − | 0.424547i | −0.644136 | − | 0.764911i | \(-0.722783\pi\) |
−0.940294 | + | 0.340365i | \(0.889449\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.2846 | − | 5.93782i | 0.971384 | − | 0.237513i | ||||
\(626\) | 43.3013 | + | 25.0000i | 1.73067 | + | 0.999201i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 47.0526 | + | 12.6077i | 1.87760 | + | 0.503102i | ||||
\(629\) | −1.53590 | −0.0612403 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −34.9019 | − | 20.1506i | −1.38613 | − | 0.800284i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.62436 | + | 25.1865i | −0.0643593 | + | 0.997927i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −8.00000 | − | 24.0000i | −0.316228 | − | 0.948683i | ||||
\(641\) | 19.6506 | + | 34.0359i | 0.776153 | + | 1.34434i | 0.934144 | + | 0.356897i | \(0.116165\pi\) |
−0.157991 | + | 0.987441i | \(0.550502\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(648\) | −24.5885 | + | 6.58846i | −0.965926 | + | 0.258819i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 17.0000 | − | 19.0000i | 0.666795 | − | 0.745241i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 12.8109 | + | 47.8109i | 0.501329 | + | 1.87098i | 0.491220 | + | 0.871036i | \(0.336551\pi\) |
0.0101092 | + | 0.999949i | \(0.496782\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 41.3205 | − | 23.8564i | 1.61329 | − | 0.931436i | ||||
\(657\) | 4.79423 | + | 1.28461i | 0.187041 | + | 0.0501174i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12.6506 | − | 7.30385i | −0.492053 | − | 0.284087i | 0.233373 | − | 0.972387i | \(-0.425024\pi\) |
−0.725426 | + | 0.688301i | \(0.758357\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −23.4904 | + | 40.6865i | −0.910234 | + | 1.57657i | ||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.91858 | − | 10.8923i | −0.112503 | − | 0.419867i | 0.886585 | − | 0.462566i | \(-0.153071\pi\) |
−0.999088 | + | 0.0426985i | \(0.986405\pi\) | |||||||
\(674\) | −18.5622 | + | 32.1506i | −0.714988 | + | 1.23840i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3.33975 | − | 25.7846i | 0.128452 | − | 0.991716i | ||||
\(677\) | 25.0000 | + | 25.0000i | 0.960828 | + | 0.960828i | 0.999261 | − | 0.0384331i | \(-0.0122367\pi\) |
−0.0384331 | + | 0.999261i | \(0.512237\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −0.483340 | − | 0.732051i | −0.0185352 | − | 0.0280729i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6.01666 | + | 29.4019i | −0.229885 | + | 1.12339i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 25.5718 | + | 8.65064i | 0.974208 | + | 0.329563i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(692\) | −40.9808 | + | 10.9808i | −1.55785 | + | 0.417426i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.16987 | − | 1.16987i | 0.0443121 | − | 0.0443121i | ||||
\(698\) | 13.6603 | + | 3.66025i | 0.517048 | + | 0.138543i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 52.0000 | 1.96401 | 0.982006 | − | 0.188847i | \(-0.0604752\pi\) | ||||
0.982006 | + | 0.188847i | \(0.0604752\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −26.1506 | − | 45.2942i | −0.984192 | − | 1.70467i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 11.5526 | + | 20.0096i | 0.433865 | + | 0.751477i | 0.997202 | − | 0.0747503i | \(-0.0238160\pi\) |
−0.563337 | + | 0.826227i | \(0.690483\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 27.3205 | − | 7.32051i | 1.02388 | − | 0.274348i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(720\) | −26.7846 | + | 1.60770i | −0.998203 | + | 0.0599153i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −25.9545 | − | 6.95448i | −0.965926 | − | 0.258819i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −14.4115 | + | 8.32051i | −0.535601 | + | 0.309229i | ||||
\(725\) | −49.0167 | − | 20.9378i | −1.82043 | − | 0.777611i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.0000i | 1.00000i | ||||||||
\(730\) | 4.67949 | + | 2.33975i | 0.173196 | + | 0.0865979i | ||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 7.15064 | + | 7.15064i | 0.264115 | + | 0.264115i | 0.826723 | − | 0.562609i | \(-0.190202\pi\) |
−0.562609 | + | 0.826723i | \(0.690202\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −13.0981 | − | 48.8827i | −0.482147 | − | 1.79940i | ||||
\(739\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(740\) | −32.8564 | + | 37.0526i | −1.20783 | + | 1.36208i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 41.2846 | − | 27.2583i | 1.51255 | − | 0.998668i | ||||
\(746\) | − | 44.0526i | − | 1.61288i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −53.3013 | + | 10.6603i | −1.94112 | + | 0.388224i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −47.8109 | + | 12.8109i | −1.73772 | + | 0.465620i | −0.981937 | − | 0.189207i | \(-0.939408\pi\) |
−0.755779 | + | 0.654827i | \(0.772742\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −34.6410 | + | 20.0000i | −1.25574 | + | 0.724999i | −0.972243 | − | 0.233975i | \(-0.924827\pi\) |
−0.283493 | + | 0.958974i | \(0.591493\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.882686 | + | 0.294229i | −0.0319136 | + | 0.0106379i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 25.0000 | − | 43.3013i | 0.901523 | − | 1.56148i | 0.0760054 | − | 0.997107i | \(-0.475783\pi\) |
0.825518 | − | 0.564376i | \(-0.190883\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −10.3397 | + | 10.3397i | −0.372136 | + | 0.372136i | ||||
\(773\) | −14.2750 | + | 53.2750i | −0.513436 | + | 1.91617i | −0.133887 | + | 0.990997i | \(0.542746\pi\) |
−0.379549 | + | 0.925172i | \(0.623921\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 26.0000 | + | 45.0333i | 0.933346 | + | 1.61660i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −46.8827 | + | 12.5622i | −1.68083 | + | 0.450376i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 24.2487 | − | 14.0000i | 0.866025 | − | 0.500000i | ||||
\(785\) | 36.1340 | − | 40.7487i | 1.28968 | − | 1.45438i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(788\) | −26.0000 | − | 26.0000i | −0.926212 | − | 0.926212i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.32051 | + | 7.98076i | −0.188937 | + | 0.283405i | ||||
\(794\) | 26.0000i | 0.922705i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −5.49038 | + | 20.4904i | −0.194479 | + | 0.725807i | 0.797922 | + | 0.602761i | \(0.205933\pi\) |
−0.992401 | + | 0.123045i | \(0.960734\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −28.0000 | − | 4.00000i | −0.989949 | − | 0.141421i | ||||
\(801\) | − | 30.0000i | − | 1.06000i | ||||||
\(802\) | 7.95448 | − | 29.6865i | 0.280883 | − | 1.04827i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −50.0526 | + | 13.4115i | −1.76084 | + | 0.471816i | ||||
\(809\) | −31.7487 | − | 18.3301i | −1.11623 | − | 0.644453i | −0.175791 | − | 0.984428i | \(-0.556248\pi\) |
−0.940435 | + | 0.339975i | \(0.889582\pi\) | |||||||
\(810\) | −5.70577 | + | 27.8827i | −0.200480 | + | 0.979698i | ||||
\(811\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 25.1962 | − | 25.1962i | 0.880963 | − | 0.880963i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −3.19615 | − | 53.2487i | −0.111614 | − | 1.85953i | ||||
\(821\) | −43.3013 | − | 25.0000i | −1.51122 | − | 0.872506i | −0.999914 | − | 0.0131101i | \(-0.995827\pi\) |
−0.511311 | − | 0.859396i | \(-0.670840\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 38.3827 | + | 22.1603i | 1.33309 | + | 0.769657i | 0.985771 | − | 0.168091i | \(-0.0537604\pi\) |
0.347314 | + | 0.937749i | \(0.387094\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −25.8564 | + | 12.7846i | −0.896410 | + | 0.443227i | ||||
\(833\) | 0.686533 | − | 0.686533i | 0.0237870 | − | 0.0237870i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 42.3205 | + | 73.3013i | 1.45933 | + | 2.52763i | ||||
\(842\) | 12.6340 | − | 3.38526i | 0.435396 | − | 0.116664i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −24.1147 | − | 16.2321i | −0.829572 | − | 0.558400i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −7.75129 | − | 28.9282i | −0.266180 | − | 0.993399i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −0.973721 | + | 0.117314i | −0.0333983 | + | 0.00402384i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −24.8301 | − | 24.8301i | −0.850167 | − | 0.850167i | 0.139986 | − | 0.990153i | \(-0.455294\pi\) |
−0.990153 | + | 0.139986i | \(0.955294\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −41.0788 | − | 41.0788i | −1.40323 | − | 1.40323i | −0.789584 | − | 0.613642i | \(-0.789704\pi\) |
−0.613642 | − | 0.789584i | \(-0.710296\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −9.50962 | + | 46.4711i | −0.323337 | + | 1.58007i | ||||
\(866\) | − | 45.2295i | − | 1.53696i | ||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 40.0000 | + | 40.0000i | 1.35457 | + | 1.35457i | ||||
\(873\) | 53.2750 | − | 14.2750i | 1.80309 | − | 0.483135i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 57.1147 | + | 15.3038i | 1.92863 | + | 0.516774i | 0.979260 | + | 0.202606i | \(0.0649409\pi\) |
0.949367 | + | 0.314169i | \(0.101726\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 13.6506 | − | 23.6436i | 0.459902 | − | 0.796573i | −0.539054 | − | 0.842271i | \(-0.681218\pi\) |
0.998955 | + | 0.0456985i | \(0.0145514\pi\) | |||||||
\(882\) | −7.68653 | − | 28.6865i | −0.258819 | − | 0.965926i | ||||
\(883\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(884\) | −0.751289 | + | 0.660254i | −0.0252686 | + | 0.0222067i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 6.33975 | − | 30.9808i | 0.212509 | − | 1.03848i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 40.0000 | − | 40.0000i | 1.33482 | − | 1.33482i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −11.7846 | + | 27.5885i | −0.392820 | + | 0.919615i | ||||
\(901\) | −0.519238 | − | 0.899346i | −0.0172983 | − | 0.0299616i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 13.2679 | + | 22.9808i | 0.441285 | + | 0.764329i | ||||
\(905\) | 1.11474 | + | 18.5718i | 0.0370551 | + | 0.617347i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 54.9615i | 1.82296i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 22.7776 | − | 13.1506i | 0.753415 | − | 0.434984i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −51.9615 | + | 30.0000i | −1.71686 | + | 0.991228i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 22.9090 | + | 22.9090i | 0.754467 | + | 0.754467i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 20.6244 | + | 51.3827i | 0.678125 | + | 1.68945i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 42.6410 | + | 42.6410i | 1.39976 | + | 1.39976i | ||||
\(929\) | −9.91858 | − | 17.1795i | −0.325418 | − | 0.563641i | 0.656179 | − | 0.754606i | \(-0.272172\pi\) |
−0.981597 | + | 0.190965i | \(0.938838\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 3.66025 | − | 13.6603i | 0.119896 | − | 0.447456i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 6.00000 | + | 30.0000i | 0.196116 | + | 0.980581i | ||||
\(937\) | 39.7391 | + | 39.7391i | 1.29822 | + | 1.29822i | 0.929567 | + | 0.368652i | \(0.120181\pi\) |
0.368652 | + | 0.929567i | \(0.379819\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 20.0000i | 0.651981i | 0.945373 | + | 0.325991i | \(0.105698\pi\) | ||||
−0.945373 | + | 0.325991i | \(0.894302\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.91154 | − | 5.65064i | 0.0620513 | − | 0.183427i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −20.4904 | − | 5.49038i | −0.663749 | − | 0.177851i | −0.0888114 | − | 0.996048i | \(-0.528307\pi\) |
−0.574937 | + | 0.818198i | \(0.694974\pi\) | |||||||
\(954\) | −31.7654 | −1.02844 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −31.0000 | −1.00000 | ||||||||
\(962\) | 46.9808 | + | 31.3205i | 1.51472 | + | 1.00981i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 21.9282 | − | 37.9808i | 0.706260 | − | 1.22328i | ||||
\(965\) | 5.16987 | + | 15.5096i | 0.166424 | + | 0.499272i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(968\) | 8.05256 | − | 30.0526i | 0.258819 | − | 0.965926i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 58.0333 | − | 3.48334i | 1.86334 | − | 0.111843i | ||||
\(971\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 10.6410 | 0.340611 | ||||||||
\(977\) | −16.0359 | − | 59.8468i | −0.513034 | − | 1.91467i | −0.385063 | − | 0.922890i | \(-0.625820\pi\) |
−0.127971 | − | 0.991778i | \(-0.540847\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −1.87564 | − | 31.2487i | −0.0599153 | − | 0.998203i | ||||
\(981\) | 51.9615 | − | 30.0000i | 1.65900 | − | 0.957826i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −39.0000 | + | 13.0000i | −1.24264 | + | 0.414214i | ||||
\(986\) | 1.81089 | + | 1.04552i | 0.0576705 | + | 0.0332961i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 16.3038 | − | 60.8468i | 0.516348 | − | 1.92704i | 0.190022 | − | 0.981780i | \(-0.439144\pi\) |
0.326326 | − | 0.945257i | \(-0.394189\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 260.2.bg.a.147.1 | yes | 4 | |
4.3 | odd | 2 | CM | 260.2.bg.a.147.1 | yes | 4 | |
5.3 | odd | 4 | 260.2.bg.b.43.1 | yes | 4 | ||
13.10 | even | 6 | 260.2.bg.b.127.1 | yes | 4 | ||
20.3 | even | 4 | 260.2.bg.b.43.1 | yes | 4 | ||
52.23 | odd | 6 | 260.2.bg.b.127.1 | yes | 4 | ||
65.23 | odd | 12 | inner | 260.2.bg.a.23.1 | ✓ | 4 | |
260.23 | even | 12 | inner | 260.2.bg.a.23.1 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
260.2.bg.a.23.1 | ✓ | 4 | 65.23 | odd | 12 | inner | |
260.2.bg.a.23.1 | ✓ | 4 | 260.23 | even | 12 | inner | |
260.2.bg.a.147.1 | yes | 4 | 1.1 | even | 1 | trivial | |
260.2.bg.a.147.1 | yes | 4 | 4.3 | odd | 2 | CM | |
260.2.bg.b.43.1 | yes | 4 | 5.3 | odd | 4 | ||
260.2.bg.b.43.1 | yes | 4 | 20.3 | even | 4 | ||
260.2.bg.b.127.1 | yes | 4 | 13.10 | even | 6 | ||
260.2.bg.b.127.1 | yes | 4 | 52.23 | odd | 6 |