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 | 127.1 | ||
Root | \(-0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 260.127 |
Dual form | 260.2.bg.b.43.1 |
$q$-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 \(\left(\mathbb{Z}/260\mathbb{Z}\right)^\times\).
\(n\) | \(41\) | \(131\) | \(157\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.36603 | + | 0.366025i | 0.965926 | + | 0.258819i | ||||
\(3\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(4\) | 1.73205 | + | 1.00000i | 0.866025 | + | 0.500000i | ||||
\(5\) | −0.133975 | − | 2.23205i | −0.0599153 | − | 0.998203i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(8\) | 2.00000 | + | 2.00000i | 0.707107 | + | 0.707107i | ||||
\(9\) | 2.59808 | + | 1.50000i | 0.866025 | + | 0.500000i | ||||
\(10\) | 0.633975 | − | 3.09808i | 0.200480 | − | 0.979698i | ||||
\(11\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.23205 | − | 1.59808i | −0.896410 | − | 0.443227i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.00000 | + | 3.46410i | 0.500000 | + | 0.866025i | ||||
\(17\) | −0.133975 | + | 0.0358984i | −0.0324936 | + | 0.00870664i | −0.275029 | − | 0.961436i | \(-0.588688\pi\) |
0.242536 | + | 0.970143i | \(0.422021\pi\) | |||||||
\(18\) | 3.00000 | + | 3.00000i | 0.707107 | + | 0.707107i | ||||
\(19\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(20\) | 2.00000 | − | 4.00000i | 0.447214 | − | 0.894427i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(24\) | 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 | −0.785872 | + | 0.618389i | \(0.787786\pi\) |
−0.928477 | + | 0.371391i | \(0.878881\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(32\) | 1.46410 | + | 5.46410i | 0.258819 | + | 0.965926i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.196152 | −0.0336399 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3.00000 | + | 5.19615i | 0.500000 | + | 0.866025i | ||||
\(37\) | −10.6962 | − | 2.86603i | −1.75844 | − | 0.471172i | −0.772043 | − | 0.635571i | \(-0.780765\pi\) |
−0.986394 | + | 0.164399i | \(0.947432\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 4.19615 | − | 4.73205i | 0.663470 | − | 0.748203i | ||||
\(41\) | 10.3301 | − | 5.96410i | 1.61329 | − | 0.931436i | 0.624695 | − | 0.780869i | \(-0.285223\pi\) |
0.988600 | − | 0.150567i | \(-0.0481100\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.00000 | − | 6.00000i | 0.447214 | − | 0.894427i | ||||
\(46\) | 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 | ||||
\(50\) | −7.00000 | − | 1.00000i | −0.989949 | − | 0.141421i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −4.00000 | − | 6.00000i | −0.554700 | − | 0.832050i | ||||
\(53\) | 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 | ||||||||
\(58\) | −14.5622 | + | 3.90192i | −1.91211 | + | 0.512348i | ||||
\(59\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.33013 | − | 2.30385i | 0.170305 | − | 0.294977i | −0.768221 | − | 0.640184i | \(-0.778858\pi\) |
0.938527 | + | 0.345207i | \(0.112191\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.00000i | 1.00000i | ||||||||
\(65\) | −3.13397 | + | 7.42820i | −0.388722 | + | 0.921355i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(68\) | −0.267949 | − | 0.0717968i | −0.0324936 | − | 0.00870664i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(72\) | 2.19615 | + | 8.19615i | 0.258819 | + | 0.965926i | ||||
\(73\) | 1.16987 | + | 1.16987i | 0.136923 | + | 0.136923i | 0.772246 | − | 0.635323i | \(-0.219133\pi\) |
−0.635323 | + | 0.772246i | \(0.719133\pi\) | |||||||
\(74\) | −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 | \(0.5\pi\) | |||||||||
\(80\) | 7.46410 | − | 4.92820i | 0.834512 | − | 0.550990i | ||||
\(81\) | 4.50000 | + | 7.79423i | 0.500000 | + | 0.866025i | ||||
\(82\) | 16.2942 | − | 4.36603i | 1.79940 | − | 0.482147i | ||||
\(83\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.0980762 | + | 0.294229i | 0.0106379 | + | 0.0319136i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.00000 | + | 8.66025i | 0.529999 | + | 0.917985i | 0.999388 | + | 0.0349934i | \(0.0111410\pi\) |
−0.469389 | + | 0.882992i | \(0.655526\pi\) | |||||||
\(90\) | 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 | ||||||||
\(97\) | −4.75833 | − | 17.7583i | −0.483135 | − | 1.80309i | −0.588315 | − | 0.808632i | \(-0.700208\pi\) |
0.105180 | − | 0.994453i | \(-0.466458\pi\) | |||||||
\(98\) | −9.56218 | + | 2.56218i | −0.965926 | + | 0.258819i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −9.19615 | − | 3.92820i | −0.919615 | − | 0.392820i | ||||
\(101\) | 9.16025 | + | 15.8660i | 0.911479 | + | 1.57873i | 0.811976 | + | 0.583691i | \(0.198392\pi\) |
0.0995037 | + | 0.995037i | \(0.468274\pi\) | |||||||
\(102\) | 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 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 20.0000 | 1.91565 | 0.957826 | − | 0.287348i | \(-0.0927736\pi\) | ||||
0.957826 | + | 0.287348i | \(0.0927736\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.42820 | + | 9.06218i | 0.228426 | + | 0.852498i | 0.981003 | + | 0.193993i | \(0.0621440\pi\) |
−0.752577 | + | 0.658505i | \(0.771189\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −21.3205 | −1.97956 | ||||||||
\(117\) | −6.00000 | − | 9.00000i | −0.554700 | − | 0.832050i | ||||
\(118\) | 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 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(128\) | −2.92820 | + | 10.9282i | −0.258819 | + | 0.965926i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −7.00000 | + | 9.00000i | −0.613941 | + | 0.789352i | ||||
\(131\) | 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 | ||||
\(137\) | 3.47372 | + | 12.9641i | 0.296780 | + | 1.10760i | 0.939793 | + | 0.341743i | \(0.111017\pi\) |
−0.643013 | + | 0.765855i | \(0.722316\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 12.0000i | 1.00000i | ||||||||
\(145\) | 13.1340 | + | 19.8923i | 1.09072 | + | 1.65197i | ||||
\(146\) | 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 | 0.0870170 | − | 0.996207i | \(-0.472267\pi\) |
0.819232 | − | 0.573462i | \(-0.194400\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.401924 | − | 0.107695i | −0.0324936 | − | 0.00870664i | ||||
\(154\) | 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 | ||||||||
\(160\) | 12.0000 | − | 4.00000i | 0.948683 | − | 0.316228i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 3.29423 | + | 12.2942i | 0.258819 | + | 0.965926i | ||||
\(163\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(164\) | 23.8564 | 1.86287 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(168\) | 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 | ||||||||
\(173\) | −5.49038 | − | 20.4904i | −0.417426 | − | 1.55785i | −0.779926 | − | 0.625871i | \(-0.784744\pi\) |
0.362500 | − | 0.931984i | \(-0.381923\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 3.66025 | + | 13.6603i | 0.274348 | + | 1.02388i | ||||
\(179\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(180\) | 11.1962 | − | 7.39230i | 0.834512 | − | 0.550990i | ||||
\(181\) | 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 | ||||||||
\(185\) | −4.96410 | + | 24.2583i | −0.364968 | + | 1.78351i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.89230 | − | 7.06218i | 0.136211 | − | 0.508347i | −0.863779 | − | 0.503871i | \(-0.831909\pi\) |
0.999990 | − | 0.00447566i | \(-0.00142465\pi\) | |||||||
\(194\) | − | 26.0000i | − | 1.86669i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −14.0000 | −1.00000 | ||||||||
\(197\) | 17.7583 | + | 4.75833i | 1.26523 | + | 0.339017i | 0.828201 | − | 0.560431i | \(-0.189365\pi\) |
0.437028 | + | 0.899448i | \(0.356031\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(200\) | −11.1244 | − | 8.73205i | −0.786611 | − | 0.617449i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 6.70577 | + | 25.0263i | 0.471816 | + | 1.76084i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −14.6962 | − | 22.2583i | −1.02642 | − | 1.55459i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −0.928203 | − | 14.3923i | −0.0643593 | − | 0.997927i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(212\) | 14.4641 | − | 3.87564i | 0.993399 | − | 0.266180i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 27.3205 | + | 7.32051i | 1.85038 | + | 0.495807i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.490381 | + | 0.0980762i | 0.0329866 | + | 0.00659732i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −13.7942 | − | 5.89230i | −0.919615 | − | 0.392820i | ||||
\(226\) | 13.2679i | 0.882571i | ||||||||
\(227\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −30.0000 | −1.98246 | −0.991228 | − | 0.132164i | \(-0.957808\pi\) | ||||
−0.991228 | + | 0.132164i | \(0.957808\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −29.1244 | − | 7.80385i | −1.91211 | − | 0.512348i | ||||
\(233\) | −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 | −0.257663 | − | 0.966235i | \(-0.582952\pi\) |
−0.965615 | + | 0.259975i | \(0.916286\pi\) | |||||||
\(242\) | 11.0000 | − | 11.0000i | 0.707107 | − | 0.707107i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 4.60770 | − | 2.66025i | 0.294977 | − | 0.170305i | ||||
\(245\) | 8.62436 | + | 13.0622i | 0.550990 | + | 0.834512i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.29423 | + | 15.7583i | −0.0818542 | + | 0.996644i | ||||
\(251\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.00000 | + | 13.8564i | −0.500000 | + | 0.866025i | ||||
\(257\) | −8.13397 | + | 30.3564i | −0.507383 | + | 1.89358i | −0.0623783 | + | 0.998053i | \(0.519869\pi\) |
−0.445005 | + | 0.895528i | \(0.646798\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −12.8564 | + | 9.73205i | −0.797320 | + | 0.603556i | ||||
\(261\) | −31.9808 | −1.97956 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(264\) | 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 | \(-0.624619\pi\) |
−0.991288 | + | 0.131713i | \(0.957952\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(272\) | −0.392305 | − | 0.392305i | −0.0237870 | − | 0.0237870i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 18.9808i | 1.14667i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −30.6244 | + | 8.20577i | −1.84004 | + | 0.493037i | −0.998861 | − | 0.0477206i | \(-0.984804\pi\) |
−0.841178 | + | 0.540758i | \(0.818138\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 22.7128i | − | 1.35493i | −0.735554 | − | 0.677466i | \(-0.763078\pi\) | ||
0.735554 | − | 0.677466i | \(-0.236922\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −4.39230 | + | 16.3923i | −0.258819 | + | 0.965926i | ||||
\(289\) | −14.7058 | + | 8.49038i | −0.865045 | + | 0.499434i | ||||
\(290\) | 10.6603 | + | 31.9808i | 0.625992 | + | 1.87798i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0.856406 | + | 3.19615i | 0.0501174 | + | 0.187041i | ||||
\(293\) | 30.7224 | − | 8.23205i | 1.79482 | − | 0.480922i | 0.801673 | − | 0.597763i | \(-0.203944\pi\) |
0.993151 | + | 0.116841i | \(0.0372769\pi\) | |||||||
\(294\) | 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 | ||||||||
\(305\) | −5.32051 | − | 2.66025i | −0.304651 | − | 0.152326i | ||||
\(306\) | −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 | \(-0.454682\pi\) |
0.989882 | − | 0.141890i | \(-0.0453179\pi\) | |||||||
\(318\) | 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 | ||||||||
\(325\) | 17.0000 | + | 6.00000i | 0.942990 | + | 0.332820i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 32.5885 | + | 8.73205i | 1.79940 | + | 0.482147i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(332\) | 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 | \(0.496432\pi\) | |||||||
\(338\) | 7.00000 | + | 17.0000i | 0.380750 | + | 0.924678i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −0.124356 | + | 0.607695i | −0.00674413 | + | 0.0329569i | ||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 30.0000i | − | 1.61281i | ||||||
\(347\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5.00000 | − | 8.66025i | −0.267644 | − | 0.463573i | 0.700609 | − | 0.713545i | \(-0.252912\pi\) |
−0.968253 | + | 0.249973i | \(0.919578\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −9.57180 | + | 35.7224i | −0.509455 | + | 1.90131i | −0.0836583 | + | 0.996495i | \(0.526660\pi\) |
−0.425797 | + | 0.904819i | \(0.640006\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 20.0000i | 1.06000i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(360\) | 18.0000 | − | 6.00000i | 0.948683 | − | 0.316228i | ||||
\(361\) | −9.50000 | − | 16.4545i | −0.500000 | − | 0.866025i | ||||
\(362\) | 11.3660 | + | 3.04552i | 0.597385 | + | 0.160069i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.45448 | − | 2.76795i | 0.128473 | − | 0.144881i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 35.7846 | 1.86287 | ||||||||
\(370\) | −15.6603 | + | 31.3205i | −0.814138 | + | 1.62828i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.06218 | + | 30.0885i | 0.417444 | + | 1.55792i | 0.779890 | + | 0.625917i | \(0.215275\pi\) |
−0.362446 | + | 0.932005i | \(0.618058\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 38.3564 | − | 2.47372i | 1.97546 | − | 0.127403i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 5.16987 | − | 8.95448i | 0.263140 | − | 0.455771i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 9.51666 | − | 35.5167i | 0.483135 | − | 1.80309i | ||||
\(389\) | 34.3205i | 1.74012i | 0.492947 | + | 0.870059i | \(0.335920\pi\) | ||||
−0.492947 | + | 0.870059i | \(0.664080\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −19.1244 | − | 5.12436i | −0.965926 | − | 0.258819i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 22.5167 | + | 13.0000i | 1.13437 | + | 0.654931i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.75833 | + | 17.7583i | 0.238814 | + | 0.891265i | 0.976392 | + | 0.216004i | \(0.0693024\pi\) |
−0.737579 | + | 0.675261i | \(0.764031\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −12.0000 | − | 16.0000i | −0.600000 | − | 0.800000i | ||||
\(401\) | −18.8205 | + | 10.8660i | −0.939851 | + | 0.542623i | −0.889914 | − | 0.456129i | \(-0.849236\pi\) |
−0.0499376 | + | 0.998752i | \(0.515902\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 36.6410i | 1.82296i | ||||||||
\(405\) | 16.7942 | − | 11.0885i | 0.834512 | − | 0.550990i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12.5981 | − | 21.8205i | 0.622935 | − | 1.07895i | −0.366002 | − | 0.930614i | \(-0.619274\pi\) |
0.988936 | − | 0.148340i | \(-0.0473931\pi\) | |||||||
\(410\) | −11.9282 | − | 35.7846i | −0.589092 | − | 1.76728i | ||||
\(411\) | 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 | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.24871i | 0.450755i | 0.974272 | + | 0.225377i | \(0.0723615\pi\) | ||||
−0.974272 | + | 0.225377i | \(0.927639\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 21.1769 | 1.02844 | ||||||||
\(425\) | 0.643594 | − | 0.258330i | 0.0312189 | − | 0.0125309i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8.27757 | + | 30.8923i | 0.397795 | + | 1.48459i | 0.816968 | + | 0.576683i | \(0.195653\pi\) |
−0.419173 | + | 0.907906i | \(0.637680\pi\) | |||||||
\(434\) | 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 | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −21.0000 | −1.00000 | ||||||||
\(442\) | 0.633975 | + | 0.313467i | 0.0301551 | + | 0.0149101i | ||||
\(443\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 18.6603 | − | 12.3205i | 0.884581 | − | 0.584048i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 20.0000 | − | 34.6410i | 0.943858 | − | 1.63481i | 0.185837 | − | 0.982581i | \(-0.440500\pi\) |
0.758021 | − | 0.652230i | \(-0.226166\pi\) | |||||||
\(450\) | −16.6865 | − | 13.0981i | −0.786611 | − | 0.617449i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −4.85641 | + | 18.1244i | −0.228426 | + | 0.852498i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −17.9641 | − | 4.81347i | −0.840325 | − | 0.225164i | −0.187112 | − | 0.982339i | \(-0.559913\pi\) |
−0.653213 | + | 0.757174i | \(0.726579\pi\) | |||||||
\(458\) | −40.9808 | − | 10.9808i | −1.91491 | − | 0.513097i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 19.8397 | + | 11.4545i | 0.924029 | + | 0.533488i | 0.884918 | − | 0.465746i | \(-0.154214\pi\) |
0.0391109 | + | 0.999235i | \(0.487547\pi\) | |||||||
\(462\) | 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 | \(0.250000\pi\) | |||||||
\(468\) | −1.39230 | − | 21.5885i | −0.0643593 | − | 0.997927i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 21.6962 | − | 5.81347i | 0.993399 | − | 0.266180i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(480\) | 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 | ||||
\(485\) | −39.0000 | + | 13.0000i | −1.77090 | + | 0.590300i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(488\) | 7.26795 | − | 1.94744i | 0.329005 | − | 0.0881565i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 7.00000 | + | 21.0000i | 0.316228 | + | 0.948683i | ||||
\(491\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(492\) | 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 | \(\pi\) | |||||||||
\(500\) | −7.53590 | + | 21.0526i | −0.337016 | + | 0.941499i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 34.1865 | − | 22.5718i | 1.52128 | − | 1.00443i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −16.5526 | − | 28.6699i | −0.733679 | − | 1.27077i | −0.955300 | − | 0.295637i | \(-0.904468\pi\) |
0.221621 | − | 0.975133i | \(-0.428865\pi\) | |||||||
\(510\) | 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 | ||||||||
\(520\) | −21.1244 | + | 8.58846i | −0.926364 | + | 0.376629i | ||||
\(521\) | −23.6410 | −1.03573 | −0.517866 | − | 0.855462i | \(-0.673273\pi\) | ||||
−0.517866 | + | 0.855462i | \(0.673273\pi\) | |||||||
\(522\) | −43.6865 | − | 11.7058i | −1.91211 | − | 0.512348i | ||||
\(523\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 19.9186 | + | 11.5000i | 0.866025 | + | 0.500000i | ||||
\(530\) | −13.0455 | − | 19.7583i | −0.566661 | − | 0.858247i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −42.9186 | + | 2.76795i | −1.85901 | + | 0.119893i | ||||
\(534\) | 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 | \(0.474796\pi\) | ||||
−0.0790969 | + | 0.996867i | \(0.525204\pi\) | |||||||
\(542\) | 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 | \(0.250000\pi\) | |||||||
\(548\) | −6.94744 | + | 25.9282i | −0.296780 | + | 1.10760i | ||||
\(549\) | 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 | ||||||||
\(557\) | 28.4545 | + | 7.62436i | 1.20566 | + | 0.323054i | 0.805056 | − | 0.593199i | \(-0.202135\pi\) |
0.400599 | + | 0.916253i | \(0.368802\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 8.31347 | − | 31.0263i | 0.350682 | − | 1.30876i | ||||
\(563\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 19.9019 | − | 6.63397i | 0.837280 | − | 0.279093i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −22.5167 | + | 13.0000i | −0.943948 | + | 0.544988i | −0.891196 | − | 0.453619i | \(-0.850133\pi\) |
−0.0527519 | + | 0.998608i | \(0.516799\pi\) | |||||||
\(570\) | 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 | \(0.679922\pi\) |
−0.844459 | + | 0.535620i | \(0.820078\pi\) | |||||||
\(578\) | −23.1962 | + | 6.21539i | −0.964833 | + | 0.258526i | ||||
\(579\) | 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 | ||||||||
\(585\) | −19.2846 | + | 14.5981i | −0.797320 | + | 0.603556i | ||||
\(586\) | 44.9808 | 1.85814 | ||||||||
\(587\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −11.4641 | − | 42.7846i | −0.471172 | − | 1.75844i | ||||
\(593\) | −2.50962 | − | 2.50962i | −0.103058 | − | 0.103058i | 0.653698 | − | 0.756756i | \(-0.273217\pi\) |
−0.756756 | + | 0.653698i | \(0.773217\pi\) | |||||||
\(594\) | 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 | 0.666120 | − | 0.745845i | \(-0.267954\pi\) |
−0.978980 | + | 0.203954i | \(0.934621\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −22.0000 | − | 11.0000i | −0.894427 | − | 0.447214i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(608\) | 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 | ||||
\(613\) | −11.2776 | + | 42.0885i | −0.455497 | + | 1.69994i | 0.231127 | + | 0.972924i | \(0.425759\pi\) |
−0.686624 | + | 0.727013i | \(0.740908\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −10.5455 | − | 39.3564i | −0.424547 | − | 1.58443i | −0.764911 | − | 0.644136i | \(-0.777217\pi\) |
0.340365 | − | 0.940294i | \(-0.389449\pi\) | |||||||
\(618\) | 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 | ||||||||
\(628\) | −12.6077 | − | 47.0526i | −0.503102 | − | 1.87760i | ||||
\(629\) | 1.53590 | 0.0612403 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 34.9019 | − | 20.1506i | 1.38613 | − | 0.800284i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 25.1865 | − | 1.62436i | 0.997927 | − | 0.0643593i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 24.7846 | + | 5.07180i | 0.979698 | + | 0.200480i | ||||
\(641\) | 19.6506 | − | 34.0359i | 0.776153 | − | 1.34434i | −0.157991 | − | 0.987441i | \(-0.550502\pi\) |
0.934144 | − | 0.356897i | \(-0.116165\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(648\) | −6.58846 | + | 24.5885i | −0.258819 | + | 0.965926i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 21.0263 | + | 14.4186i | 0.824719 | + | 0.565543i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −47.8109 | − | 12.8109i | −1.87098 | − | 0.501329i | −0.999949 | − | 0.0101092i | \(-0.996782\pi\) |
−0.871036 | − | 0.491220i | \(-0.836551\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 41.3205 | + | 23.8564i | 1.61329 | + | 0.931436i | ||||
\(657\) | 1.28461 | + | 4.79423i | 0.0501174 | + | 0.187041i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12.6506 | + | 7.30385i | −0.492053 | + | 0.284087i | −0.725426 | − | 0.688301i | \(-0.758357\pi\) |
0.233373 | + | 0.972387i | \(0.425024\pi\) | |||||||
\(662\) | 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 | ||||||||
\(673\) | 10.8923 | + | 2.91858i | 0.419867 | + | 0.112503i | 0.462566 | − | 0.886585i | \(-0.346929\pi\) |
−0.0426985 | + | 0.999088i | \(0.513595\pi\) | |||||||
\(674\) | 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 | ||||||||
\(680\) | −0.392305 | + | 0.784610i | −0.0150442 | + | 0.0300884i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 28.4711 | − | 9.49038i | 1.08783 | − | 0.362609i | ||||
\(686\) | 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 | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(692\) | 10.9808 | − | 40.9808i | 0.417426 | − | 1.55785i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.16987 | + | 1.16987i | −0.0443121 | + | 0.0443121i | ||||
\(698\) | −3.66025 | − | 13.6603i | −0.138543 | − | 0.517048i | ||||
\(699\) | 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 | \(-0.976184\pi\) |
0.563337 | + | 0.826227i | \(0.309517\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −7.32051 | + | 27.3205i | −0.274348 | + | 1.02388i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(720\) | 26.7846 | − | 1.60770i | 0.998203 | − | 0.0599153i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −6.95448 | − | 25.9545i | −0.258819 | − | 0.965926i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 14.4115 | + | 8.32051i | 0.535601 | + | 0.309229i | ||||
\(725\) | 42.6410 | − | 31.9808i | 1.58365 | − | 1.18774i | ||||
\(726\) | 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 | ||||||||
\(730\) | 4.36603 | − | 2.88269i | 0.161594 | − | 0.106693i | ||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7.15064 | − | 7.15064i | −0.264115 | − | 0.264115i | 0.562609 | − | 0.826723i | \(-0.309798\pi\) |
−0.826723 | + | 0.562609i | \(0.809798\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 48.8827 | + | 13.0981i | 1.79940 | + | 0.482147i | ||||
\(739\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(740\) | −32.8564 | + | 37.0526i | −1.20783 | + | 1.36208i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −44.2487 | − | 22.1244i | −1.62115 | − | 0.810574i | ||||
\(746\) | 44.0526i | 1.61288i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 53.3013 | + | 10.6603i | 1.94112 | + | 0.388224i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 12.8109 | − | 47.8109i | 0.465620 | − | 1.73772i | −0.189207 | − | 0.981937i | \(-0.560592\pi\) |
0.654827 | − | 0.755779i | \(-0.272742\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −34.6410 | − | 20.0000i | −1.25574 | − | 0.724999i | −0.283493 | − | 0.958974i | \(-0.591493\pi\) |
−0.972243 | + | 0.233975i | \(0.924827\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.186533 | + | 0.911543i | −0.00674413 | + | 0.0329569i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −25.0000 | − | 43.3013i | −0.901523 | − | 1.56148i | −0.825518 | − | 0.564376i | \(-0.809117\pi\) |
−0.0760054 | − | 0.997107i | \(-0.524217\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 10.3397 | − | 10.3397i | 0.372136 | − | 0.372136i | ||||
\(773\) | −53.2750 | + | 14.2750i | −1.91617 | + | 0.513436i | −0.925172 | + | 0.379549i | \(0.876079\pi\) |
−0.990997 | + | 0.133887i | \(0.957254\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 26.0000 | − | 45.0333i | 0.933346 | − | 1.61660i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −12.5622 | + | 46.8827i | −0.450376 | + | 1.68083i | ||||
\(779\) | 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 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(788\) | 26.0000 | + | 26.0000i | 0.926212 | + | 0.926212i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7.98076 | + | 5.32051i | −0.283405 | + | 0.188937i | ||||
\(794\) | 26.0000i | 0.922705i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 20.4904 | − | 5.49038i | 0.725807 | − | 0.194479i | 0.123045 | − | 0.992401i | \(-0.460734\pi\) |
0.602761 | + | 0.797922i | \(0.294067\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −10.5359 | − | 26.2487i | −0.372500 | − | 0.928032i | ||||
\(801\) | 30.0000i | 1.06000i | ||||||||
\(802\) | −29.6865 | + | 7.95448i | −1.04827 | + | 0.280883i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −13.4115 | + | 50.0526i | −0.471816 | + | 1.76084i | ||||
\(809\) | 31.7487 | − | 18.3301i | 1.11623 | − | 0.644453i | 0.175791 | − | 0.984428i | \(-0.443752\pi\) |
0.940435 | + | 0.339975i | \(0.110418\pi\) | |||||||
\(810\) | 27.0000 | − | 9.00000i | 0.948683 | − | 0.316228i | ||||
\(811\) | 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 | −0.511311 | + | 0.859396i | \(0.670840\pi\) |
−0.999914 | + | 0.0131101i | \(0.995827\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(824\) | 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 | \(-0.946240\pi\) |
−0.347314 | + | 0.937749i | \(0.612906\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 12.7846 | − | 25.8564i | 0.443227 | − | 0.896410i | ||||
\(833\) | 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 | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 42.3205 | − | 73.3013i | 1.45933 | − | 2.52763i | ||||
\(842\) | −3.38526 | + | 12.6340i | −0.116664 | + | 0.435396i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 22.0000 | − | 19.0000i | 0.756823 | − | 0.653620i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 28.9282 | + | 7.75129i | 0.993399 | + | 0.266180i | ||||
\(849\) | 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 | 0.990153 | − | 0.139986i | \(-0.0447058\pi\) |
−0.139986 | + | 0.990153i | \(0.544706\pi\) | |||||||
\(854\) | 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 | ||||||||
\(865\) | −45.0000 | + | 15.0000i | −1.53005 | + | 0.510015i | ||||
\(866\) | 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 | ||||
\(873\) | 14.2750 | − | 53.2750i | 0.483135 | − | 1.80309i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 15.3038 | + | 57.1147i | 0.516774 | + | 1.92863i | 0.314169 | + | 0.949367i | \(0.398274\pi\) |
0.202606 | + | 0.979260i | \(0.435059\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 13.6506 | + | 23.6436i | 0.459902 | + | 0.796573i | 0.998955 | − | 0.0456985i | \(-0.0145514\pi\) |
−0.539054 | + | 0.842271i | \(0.681218\pi\) | |||||||
\(882\) | −28.6865 | − | 7.68653i | −0.965926 | − | 0.258819i | ||||
\(883\) | 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 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 30.0000 | − | 10.0000i | 1.00560 | − | 0.335201i | ||||
\(891\) | 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 | ||||||||
\(900\) | −18.0000 | − | 24.0000i | −0.600000 | − | 0.800000i | ||||
\(901\) | −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 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(908\) | 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 | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 22.9090 | + | 22.9090i | 0.754467 | + | 0.754467i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 54.8109 | + | 7.83013i | 1.80217 | + | 0.257453i | ||||
\(926\) | 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 | \(-0.727828\pi\) |
0.981597 | + | 0.190965i | \(0.0611616\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −13.6603 | + | 3.66025i | −0.447456 | + | 0.119896i | ||||
\(933\) | 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 | \(-0.894302\pi\) | ||
0.945373 | − | 0.325991i | \(-0.105698\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.91154 | − | 5.65064i | −0.0620513 | − | 0.183427i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 5.49038 | + | 20.4904i | 0.177851 | + | 0.663749i | 0.996048 | + | 0.0888114i | \(0.0283068\pi\) |
−0.818198 | + | 0.574937i | \(0.805026\pi\) | |||||||
\(954\) | 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 | ||||||||
\(962\) | 31.3205 | + | 46.9808i | 1.00981 | + | 1.51472i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −21.9282 | − | 37.9808i | −0.706260 | − | 1.22328i | ||||
\(965\) | −16.0167 | − | 3.27757i | −0.515595 | − | 0.105509i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(968\) | 30.0526 | − | 8.05256i | 0.965926 | − | 0.258819i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −58.0333 | + | 3.48334i | −1.86334 | + | 0.111843i | ||||
\(971\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 10.6410 | 0.340611 | ||||||||
\(977\) | −59.8468 | − | 16.0359i | −1.91467 | − | 0.513034i | −0.991778 | − | 0.127971i | \(-0.959153\pi\) |
−0.922890 | − | 0.385063i | \(-0.874180\pi\) | |||||||
\(978\) | 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 | ||||||||
\(985\) | 8.24167 | − | 40.2750i | 0.262601 | − | 1.28327i | ||||
\(986\) | 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 | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −60.8468 | + | 16.3038i | −1.92704 | + | 0.516348i | −0.945257 | + | 0.326326i | \(0.894189\pi\) |
−0.981780 | + | 0.190022i | \(0.939144\pi\) | |||||||
\(998\) | 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.b.127.1 | yes | 4 | |
4.3 | odd | 2 | CM | 260.2.bg.b.127.1 | yes | 4 | |
5.3 | odd | 4 | 260.2.bg.a.23.1 | ✓ | 4 | ||
13.4 | even | 6 | 260.2.bg.a.147.1 | yes | 4 | ||
20.3 | even | 4 | 260.2.bg.a.23.1 | ✓ | 4 | ||
52.43 | odd | 6 | 260.2.bg.a.147.1 | yes | 4 | ||
65.43 | odd | 12 | inner | 260.2.bg.b.43.1 | yes | 4 | |
260.43 | even | 12 | inner | 260.2.bg.b.43.1 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
260.2.bg.a.23.1 | ✓ | 4 | 5.3 | odd | 4 | ||
260.2.bg.a.23.1 | ✓ | 4 | 20.3 | even | 4 | ||
260.2.bg.a.147.1 | yes | 4 | 13.4 | even | 6 | ||
260.2.bg.a.147.1 | yes | 4 | 52.43 | odd | 6 | ||
260.2.bg.b.43.1 | yes | 4 | 65.43 | odd | 12 | inner | |
260.2.bg.b.43.1 | yes | 4 | 260.43 | even | 12 | inner | |
260.2.bg.b.127.1 | yes | 4 | 1.1 | even | 1 | trivial | |
260.2.bg.b.127.1 | yes | 4 | 4.3 | odd | 2 | CM |