Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1344,2,Mod(193,1344)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1344, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1344.193");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1344 = 2^{6} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1344.q (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(10.7318940317\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 672) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 961.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1344.961 |
Dual form | 1344.2.q.a.193.1 |
$q$-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 \(\left(\mathbb{Z}/1344\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(449\) | \(577\) | \(1093\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.500000 | − | 0.866025i | −0.288675 | − | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.00000 | + | 3.46410i | −0.894427 | + | 1.54919i | −0.0599153 | + | 0.998203i | \(0.519083\pi\) |
−0.834512 | + | 0.550990i | \(0.814250\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.50000 | + | 0.866025i | −0.944911 | + | 0.327327i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.00000 | + | 5.19615i | 0.904534 | + | 1.56670i | 0.821541 | + | 0.570149i | \(0.193114\pi\) |
0.0829925 | + | 0.996550i | \(0.473552\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.00000 | −1.38675 | −0.693375 | − | 0.720577i | \(-0.743877\pi\) | ||||
−0.693375 | + | 0.720577i | \(0.743877\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 4.00000 | 1.03280 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.00000 | − | 1.73205i | −0.242536 | − | 0.420084i | 0.718900 | − | 0.695113i | \(-0.244646\pi\) |
−0.961436 | + | 0.275029i | \(0.911312\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.500000 | − | 0.866025i | 0.114708 | − | 0.198680i | −0.802955 | − | 0.596040i | \(-0.796740\pi\) |
0.917663 | + | 0.397360i | \(0.130073\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.00000 | + | 1.73205i | 0.436436 | + | 0.377964i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.00000 | − | 5.19615i | 0.625543 | − | 1.08347i | −0.362892 | − | 0.931831i | \(-0.618211\pi\) |
0.988436 | − | 0.151642i | \(-0.0484560\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −5.50000 | − | 9.52628i | −1.10000 | − | 1.90526i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.50000 | + | 2.59808i | 0.269408 | + | 0.466628i | 0.968709 | − | 0.248199i | \(-0.0798387\pi\) |
−0.699301 | + | 0.714827i | \(0.746505\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.00000 | − | 5.19615i | 0.522233 | − | 0.904534i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.00000 | − | 10.3923i | 0.338062 | − | 1.75662i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.50000 | − | 2.59808i | 0.246598 | − | 0.427121i | −0.715981 | − | 0.698119i | \(-0.754020\pi\) |
0.962580 | + | 0.270998i | \(0.0873538\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.50000 | + | 4.33013i | 0.400320 | + | 0.693375i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.00000 | −0.937043 | −0.468521 | − | 0.883452i | \(-0.655213\pi\) | ||||
−0.468521 | + | 0.883452i | \(0.655213\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.00000 | −0.762493 | −0.381246 | − | 0.924473i | \(-0.624505\pi\) | ||||
−0.381246 | + | 0.924473i | \(0.624505\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.00000 | − | 3.46410i | −0.298142 | − | 0.516398i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.00000 | − | 3.46410i | 0.291730 | − | 0.505291i | −0.682489 | − | 0.730896i | \(-0.739102\pi\) |
0.974219 | + | 0.225605i | \(0.0724358\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.50000 | − | 4.33013i | 0.785714 | − | 0.618590i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.00000 | + | 1.73205i | −0.140028 | + | 0.242536i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.00000 | − | 5.19615i | −0.412082 | − | 0.713746i | 0.583036 | − | 0.812447i | \(-0.301865\pi\) |
−0.995117 | + | 0.0987002i | \(0.968532\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −24.0000 | −3.23616 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.00000 | −0.132453 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.00000 | − | 5.19615i | −0.390567 | − | 0.676481i | 0.601958 | − | 0.798528i | \(-0.294388\pi\) |
−0.992524 | + | 0.122047i | \(0.961054\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.00000 | + | 1.73205i | −0.128037 | + | 0.221766i | −0.922916 | − | 0.385002i | \(-0.874201\pi\) |
0.794879 | + | 0.606768i | \(0.207534\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.500000 | − | 2.59808i | 0.0629941 | − | 0.327327i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 10.0000 | − | 17.3205i | 1.24035 | − | 2.14834i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.50000 | + | 6.06218i | 0.427593 | + | 0.740613i | 0.996659 | − | 0.0816792i | \(-0.0260283\pi\) |
−0.569066 | + | 0.822292i | \(0.692695\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6.00000 | −0.722315 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 16.0000 | 1.89885 | 0.949425 | − | 0.313993i | \(-0.101667\pi\) | ||||
0.949425 | + | 0.313993i | \(0.101667\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.50000 | + | 2.59808i | 0.175562 | + | 0.304082i | 0.940356 | − | 0.340193i | \(-0.110493\pi\) |
−0.764794 | + | 0.644275i | \(0.777159\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −5.50000 | + | 9.52628i | −0.635085 | + | 1.10000i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −12.0000 | − | 10.3923i | −1.36753 | − | 1.18431i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.50000 | + | 9.52628i | −0.618798 | + | 1.07179i | 0.370907 | + | 0.928670i | \(0.379047\pi\) |
−0.989705 | + | 0.143120i | \(0.954286\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −12.0000 | −1.31717 | −0.658586 | − | 0.752506i | \(-0.728845\pi\) | ||||
−0.658586 | + | 0.752506i | \(0.728845\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.00000 | 0.867722 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.00000 | + | 3.46410i | −0.212000 | + | 0.367194i | −0.952340 | − | 0.305038i | \(-0.901331\pi\) |
0.740341 | + | 0.672232i | \(0.234664\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 12.5000 | − | 4.33013i | 1.31036 | − | 0.453921i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.50000 | − | 2.59808i | 0.155543 | − | 0.269408i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.00000 | + | 3.46410i | 0.205196 | + | 0.355409i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.00000 | −0.609208 | −0.304604 | − | 0.952479i | \(-0.598524\pi\) | ||||
−0.304604 | + | 0.952479i | \(0.598524\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −6.00000 | −0.603023 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.00000 | + | 1.73205i | 0.0995037 | + | 0.172345i | 0.911479 | − | 0.411346i | \(-0.134941\pi\) |
−0.811976 | + | 0.583691i | \(0.801608\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.50000 | − | 9.52628i | 0.541931 | − | 0.938652i | −0.456862 | − | 0.889538i | \(-0.651027\pi\) |
0.998793 | − | 0.0491146i | \(-0.0156400\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −10.0000 | + | 3.46410i | −0.975900 | + | 0.338062i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.00000 | − | 8.66025i | 0.483368 | − | 0.837218i | −0.516449 | − | 0.856318i | \(-0.672747\pi\) |
0.999818 | + | 0.0190994i | \(0.00607989\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.50000 | − | 12.9904i | −0.718370 | − | 1.24425i | −0.961645 | − | 0.274296i | \(-0.911555\pi\) |
0.243276 | − | 0.969957i | \(-0.421778\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.00000 | −0.284747 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −16.0000 | −1.50515 | −0.752577 | − | 0.658505i | \(-0.771189\pi\) | ||||
−0.752577 | + | 0.658505i | \(0.771189\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 12.0000 | + | 20.7846i | 1.11901 | + | 1.93817i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.50000 | − | 4.33013i | 0.231125 | − | 0.400320i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.00000 | + | 3.46410i | 0.366679 | + | 0.317554i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −12.5000 | + | 21.6506i | −1.13636 | + | 1.96824i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.00000 | + | 5.19615i | 0.270501 | + | 0.468521i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 24.0000 | 2.14663 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.00000 | −0.621150 | −0.310575 | − | 0.950549i | \(-0.600522\pi\) | ||||
−0.310575 | + | 0.950549i | \(0.600522\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.50000 | + | 4.33013i | 0.220113 | + | 0.381246i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.00000 | − | 5.19615i | 0.262111 | − | 0.453990i | −0.704692 | − | 0.709514i | \(-0.748915\pi\) |
0.966803 | + | 0.255524i | \(0.0822479\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.500000 | + | 2.59808i | −0.0433555 | + | 0.225282i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.00000 | + | 3.46410i | −0.172133 | + | 0.298142i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.00000 | + | 10.3923i | 0.512615 | + | 0.887875i | 0.999893 | + | 0.0146279i | \(0.00465636\pi\) |
−0.487278 | + | 0.873247i | \(0.662010\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.00000 | −0.424094 | −0.212047 | − | 0.977259i | \(-0.568013\pi\) | ||||
−0.212047 | + | 0.977259i | \(0.568013\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.00000 | −0.336861 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −15.0000 | − | 25.9808i | −1.25436 | − | 2.17262i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.50000 | − | 2.59808i | −0.536111 | − | 0.214286i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.00000 | + | 3.46410i | −0.163846 | + | 0.283790i | −0.936245 | − | 0.351348i | \(-0.885723\pi\) |
0.772399 | + | 0.635138i | \(0.219057\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.00000 | + | 6.92820i | 0.325515 | + | 0.563809i | 0.981617 | − | 0.190864i | \(-0.0611289\pi\) |
−0.656101 | + | 0.754673i | \(0.727796\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.00000 | 0.161690 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −12.0000 | −0.963863 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.00000 | + | 8.66025i | 0.399043 | + | 0.691164i | 0.993608 | − | 0.112884i | \(-0.0360089\pi\) |
−0.594565 | + | 0.804048i | \(0.702676\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.00000 | + | 5.19615i | −0.237915 | + | 0.412082i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.00000 | + | 15.5885i | −0.236433 | + | 1.22854i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.0000 | − | 17.3205i | 0.783260 | − | 1.35665i | −0.146772 | − | 0.989170i | \(-0.546888\pi\) |
0.930033 | − | 0.367477i | \(-0.119778\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 12.0000 | + | 20.7846i | 0.934199 | + | 1.61808i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −8.00000 | −0.619059 | −0.309529 | − | 0.950890i | \(-0.600171\pi\) | ||||
−0.309529 | + | 0.950890i | \(0.600171\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.0000 | 0.923077 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.500000 | + | 0.866025i | 0.0382360 | + | 0.0662266i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 11.0000 | − | 19.0526i | 0.836315 | − | 1.44854i | −0.0566411 | − | 0.998395i | \(-0.518039\pi\) |
0.892956 | − | 0.450145i | \(-0.148628\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 22.0000 | + | 19.0526i | 1.66304 | + | 1.44024i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.00000 | + | 5.19615i | −0.225494 | + | 0.390567i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −25.0000 | −1.85824 | −0.929118 | − | 0.369784i | \(-0.879432\pi\) | ||||
−0.929118 | + | 0.369784i | \(0.879432\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.00000 | 0.147844 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.00000 | + | 10.3923i | 0.441129 | + | 0.764057i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.00000 | − | 10.3923i | 0.438763 | − | 0.759961i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.50000 | + | 0.866025i | −0.181848 | + | 0.0629941i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.500000 | + | 0.866025i | 0.0359908 | + | 0.0623379i | 0.883460 | − | 0.468507i | \(-0.155208\pi\) |
−0.847469 | + | 0.530845i | \(0.821875\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −20.0000 | −1.43223 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −18.0000 | −1.28245 | −0.641223 | − | 0.767354i | \(-0.721573\pi\) | ||||
−0.641223 | + | 0.767354i | \(0.721573\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −10.0000 | − | 17.3205i | −0.708881 | − | 1.22782i | −0.965272 | − | 0.261245i | \(-0.915867\pi\) |
0.256391 | − | 0.966573i | \(-0.417466\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.50000 | − | 6.06218i | 0.246871 | − | 0.427593i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 12.0000 | − | 20.7846i | 0.838116 | − | 1.45166i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.00000 | + | 5.19615i | 0.208514 | + | 0.361158i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.00000 | 0.415029 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.0000 | −0.826114 | −0.413057 | − | 0.910705i | \(-0.635539\pi\) | ||||
−0.413057 | + | 0.910705i | \(0.635539\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −8.00000 | − | 13.8564i | −0.548151 | − | 0.949425i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 10.0000 | − | 17.3205i | 0.681994 | − | 1.18125i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.00000 | − | 5.19615i | −0.407307 | − | 0.352738i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.50000 | − | 2.59808i | 0.101361 | − | 0.175562i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.00000 | + | 8.66025i | 0.336336 | + | 0.582552i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 16.0000 | 1.07144 | 0.535720 | − | 0.844396i | \(-0.320040\pi\) | ||||
0.535720 | + | 0.844396i | \(0.320040\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 11.0000 | 0.733333 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 11.0000 | + | 19.0526i | 0.730096 | + | 1.26456i | 0.956842 | + | 0.290609i | \(0.0938578\pi\) |
−0.226746 | + | 0.973954i | \(0.572809\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.50000 | + | 9.52628i | −0.363450 | + | 0.629514i | −0.988526 | − | 0.151050i | \(-0.951735\pi\) |
0.625076 | + | 0.780564i | \(0.285068\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.00000 | + | 15.5885i | −0.197386 | + | 1.02565i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4.00000 | − | 6.92820i | 0.262049 | − | 0.453882i | −0.704737 | − | 0.709468i | \(-0.748935\pi\) |
0.966786 | + | 0.255586i | \(0.0822686\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.00000 | + | 13.8564i | 0.521862 | + | 0.903892i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 11.0000 | 0.714527 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.00000 | 0.129369 | 0.0646846 | − | 0.997906i | \(-0.479396\pi\) | ||||
0.0646846 | + | 0.997906i | \(0.479396\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.00000 | − | 8.66025i | −0.322078 | − | 0.557856i | 0.658838 | − | 0.752285i | \(-0.271048\pi\) |
−0.980917 | + | 0.194429i | \(0.937715\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.500000 | + | 0.866025i | −0.0320750 | + | 0.0555556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4.00000 | + | 27.7128i | 0.255551 | + | 1.77051i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.50000 | + | 4.33013i | −0.159071 | + | 0.275519i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 6.00000 | + | 10.3923i | 0.380235 | + | 0.658586i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 14.0000 | 0.883672 | 0.441836 | − | 0.897096i | \(-0.354327\pi\) | ||||
0.441836 | + | 0.897096i | \(0.354327\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 36.0000 | 2.26330 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −4.00000 | − | 6.92820i | −0.250490 | − | 0.433861i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6.00000 | − | 10.3923i | 0.374270 | − | 0.648254i | −0.615948 | − | 0.787787i | \(-0.711227\pi\) |
0.990217 | + | 0.139533i | \(0.0445601\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.50000 | + | 7.79423i | −0.0932055 | + | 0.484310i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 24.0000 | 1.47431 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.00000 | 0.244796 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.00000 | − | 1.73205i | −0.0609711 | − | 0.105605i | 0.833929 | − | 0.551872i | \(-0.186086\pi\) |
−0.894900 | + | 0.446267i | \(0.852753\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.00000 | + | 13.8564i | −0.485965 | + | 0.841717i | −0.999870 | − | 0.0161307i | \(-0.994865\pi\) |
0.513905 | + | 0.857847i | \(0.328199\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −10.0000 | − | 8.66025i | −0.605228 | − | 0.524142i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 33.0000 | − | 57.1577i | 1.98997 | − | 3.44674i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.500000 | + | 0.866025i | 0.0300421 | + | 0.0520344i | 0.880656 | − | 0.473757i | \(-0.157103\pi\) |
−0.850613 | + | 0.525792i | \(0.823769\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.00000 | −0.179605 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.00000 | 0.357930 | 0.178965 | − | 0.983855i | \(-0.442725\pi\) | ||||
0.178965 | + | 0.983855i | \(0.442725\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.50000 | − | 9.52628i | −0.326941 | − | 0.566279i | 0.654962 | − | 0.755662i | \(-0.272685\pi\) |
−0.981903 | + | 0.189383i | \(0.939351\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.00000 | − | 3.46410i | 0.118470 | − | 0.205196i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 15.0000 | − | 5.19615i | 0.885422 | − | 0.306719i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.50000 | − | 11.2583i | 0.382353 | − | 0.662255i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.00000 | + | 5.19615i | 0.175863 | + | 0.304604i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 12.0000 | 0.701047 | 0.350524 | − | 0.936554i | \(-0.386004\pi\) | ||||
0.350524 | + | 0.936554i | \(0.386004\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 24.0000 | 1.39733 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.00000 | + | 5.19615i | 0.174078 | + | 0.301511i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −15.0000 | + | 25.9808i | −0.867472 | + | 1.50251i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 12.5000 | − | 4.33013i | 0.720488 | − | 0.249584i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.00000 | − | 1.73205i | 0.0574485 | − | 0.0995037i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4.00000 | − | 6.92820i | −0.229039 | − | 0.396708i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −11.0000 | −0.627803 | −0.313902 | − | 0.949456i | \(-0.601636\pi\) | ||||
−0.313902 | + | 0.949456i | \(0.601636\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −11.0000 | −0.625768 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.00000 | + | 1.73205i | 0.0567048 | + | 0.0982156i | 0.892984 | − | 0.450088i | \(-0.148607\pi\) |
−0.836280 | + | 0.548303i | \(0.815274\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −15.5000 | + | 26.8468i | −0.876112 | + | 1.51747i | −0.0205381 | + | 0.999789i | \(0.506538\pi\) |
−0.855574 | + | 0.517681i | \(0.826795\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 8.00000 | + | 6.92820i | 0.450749 | + | 0.390360i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −10.0000 | + | 17.3205i | −0.561656 | + | 0.972817i | 0.435696 | + | 0.900094i | \(0.356502\pi\) |
−0.997352 | + | 0.0727229i | \(0.976831\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −10.0000 | −0.558146 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.00000 | −0.111283 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 27.5000 | + | 47.6314i | 1.52543 | + | 2.64211i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −7.50000 | + | 12.9904i | −0.414751 | + | 0.718370i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.00000 | + | 10.3923i | −0.110264 | + | 0.572946i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.50000 | + | 4.33013i | −0.137412 | + | 0.238005i | −0.926516 | − | 0.376254i | \(-0.877212\pi\) |
0.789104 | + | 0.614260i | \(0.210545\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.50000 | + | 2.59808i | 0.0821995 | + | 0.142374i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −28.0000 | −1.52980 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.00000 | 0.0544735 | 0.0272367 | − | 0.999629i | \(-0.491329\pi\) | ||||
0.0272367 | + | 0.999629i | \(0.491329\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 8.00000 | + | 13.8564i | 0.434500 | + | 0.752577i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −9.00000 | + | 15.5885i | −0.487377 | + | 0.844162i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −10.0000 | + | 15.5885i | −0.539949 | + | 0.841698i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 12.0000 | − | 20.7846i | 0.646058 | − | 1.11901i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −11.0000 | − | 19.0526i | −0.590511 | − | 1.02279i | −0.994164 | − | 0.107883i | \(-0.965593\pi\) |
0.403653 | − | 0.914912i | \(-0.367740\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −26.0000 | −1.39175 | −0.695874 | − | 0.718164i | \(-0.744983\pi\) | ||||
−0.695874 | + | 0.718164i | \(0.744983\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.00000 | −0.266880 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.00000 | + | 3.46410i | 0.106449 | + | 0.184376i | 0.914329 | − | 0.404971i | \(-0.132718\pi\) |
−0.807880 | + | 0.589347i | \(0.799385\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −32.0000 | + | 55.4256i | −1.69838 | + | 2.94169i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.00000 | − | 5.19615i | 0.0529256 | − | 0.275010i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 12.0000 | − | 20.7846i | 0.633336 | − | 1.09697i | −0.353529 | − | 0.935423i | \(-0.615019\pi\) |
0.986865 | − | 0.161546i | \(-0.0516481\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.00000 | + | 15.5885i | 0.473684 | + | 0.820445i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 25.0000 | 1.31216 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −12.0000 | −0.628109 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −13.5000 | − | 23.3827i | −0.704694 | − | 1.22057i | −0.966802 | − | 0.255528i | \(-0.917751\pi\) |
0.262108 | − | 0.965039i | \(-0.415582\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.00000 | − | 5.19615i | 0.156174 | − | 0.270501i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 12.0000 | + | 10.3923i | 0.623009 | + | 0.539542i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −14.5000 | + | 25.1147i | −0.750782 | + | 1.30039i | 0.196663 | + | 0.980471i | \(0.436990\pi\) |
−0.947444 | + | 0.319921i | \(0.896344\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −12.0000 | − | 20.7846i | −0.619677 | − | 1.07331i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −27.0000 | −1.38690 | −0.693448 | − | 0.720506i | \(-0.743909\pi\) | ||||
−0.693448 | + | 0.720506i | \(0.743909\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.50000 | + | 6.06218i | 0.179310 | + | 0.310575i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −13.0000 | + | 22.5167i | −0.664269 | + | 1.15055i | 0.315214 | + | 0.949021i | \(0.397924\pi\) |
−0.979483 | + | 0.201527i | \(0.935410\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 60.0000 | − | 20.7846i | 3.05788 | − | 1.05928i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.50000 | − | 4.33013i | 0.127082 | − | 0.220113i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2.00000 | − | 3.46410i | −0.101404 | − | 0.175637i | 0.810859 | − | 0.585241i | \(-0.199000\pi\) |
−0.912263 | + | 0.409604i | \(0.865667\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −12.0000 | −0.606866 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −6.00000 | −0.302660 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −22.0000 | − | 38.1051i | −1.10694 | − | 1.91728i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −10.5000 | + | 18.1865i | −0.526980 | + | 0.912756i | 0.472526 | + | 0.881317i | \(0.343342\pi\) |
−0.999506 | + | 0.0314391i | \(0.989991\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.50000 | − | 0.866025i | 0.125157 | − | 0.0433555i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.00000 | − | 1.73205i | 0.0499376 | − | 0.0864945i | −0.839976 | − | 0.542623i | \(-0.817431\pi\) |
0.889914 | + | 0.456129i | \(0.150764\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.50000 | − | 12.9904i | −0.373602 | − | 0.647097i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 4.00000 | 0.198762 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 18.0000 | 0.892227 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.50000 | − | 11.2583i | −0.321404 | − | 0.556689i | 0.659374 | − | 0.751815i | \(-0.270822\pi\) |
−0.980778 | + | 0.195127i | \(0.937488\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6.00000 | − | 10.3923i | 0.295958 | − | 0.512615i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 12.0000 | + | 10.3923i | 0.590481 | + | 0.511372i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 24.0000 | − | 41.5692i | 1.17811 | − | 2.04055i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.50000 | + | 4.33013i | 0.122426 | + | 0.212047i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 26.0000 | 1.27018 | 0.635092 | − | 0.772437i | \(-0.280962\pi\) | ||||
0.635092 | + | 0.772437i | \(0.280962\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −17.0000 | −0.828529 | −0.414265 | − | 0.910156i | \(-0.635961\pi\) | ||||
−0.414265 | + | 0.910156i | \(0.635961\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.00000 | + | 3.46410i | 0.0972433 | + | 0.168430i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −11.0000 | + | 19.0526i | −0.533578 | + | 0.924185i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.00000 | − | 5.19615i | 0.0483934 | − | 0.251459i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −15.0000 | + | 25.9808i | −0.724207 | + | 1.25436i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −25.0000 | −1.20142 | −0.600712 | − | 0.799466i | \(-0.705116\pi\) | ||||
−0.600712 | + | 0.799466i | \(0.705116\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3.00000 | − | 5.19615i | −0.143509 | − | 0.248566i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −12.0000 | + | 20.7846i | −0.572729 | + | 0.991995i | 0.423556 | + | 0.905870i | \(0.360782\pi\) |
−0.996284 | + | 0.0861252i | \(0.972552\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | + | 6.92820i | 0.0476190 | + | 0.329914i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −13.0000 | + | 22.5167i | −0.617649 | + | 1.06980i | 0.372265 | + | 0.928126i | \(0.378581\pi\) |
−0.989914 | + | 0.141672i | \(0.954752\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8.00000 | − | 13.8564i | −0.379236 | − | 0.656857i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4.00000 | 0.189194 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 36.0000 | 1.69895 | 0.849473 | − | 0.527633i | \(-0.176920\pi\) | ||||
0.849473 | + | 0.527633i | \(0.176920\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −18.0000 | − | 31.1769i | −0.847587 | − | 1.46806i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4.00000 | − | 6.92820i | 0.187936 | − | 0.325515i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −10.0000 | + | 51.9615i | −0.468807 | + | 2.43599i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −12.5000 | + | 21.6506i | −0.584725 | + | 1.01277i | 0.410184 | + | 0.912003i | \(0.365464\pi\) |
−0.994910 | + | 0.100771i | \(0.967869\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.00000 | − | 1.73205i | −0.0466760 | − | 0.0808452i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.00000 | 0.186299 | 0.0931493 | − | 0.995652i | \(-0.470307\pi\) | ||||
0.0931493 | + | 0.995652i | \(0.470307\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.00000 | −0.232370 | −0.116185 | − | 0.993228i | \(-0.537067\pi\) | ||||
−0.116185 | + | 0.993228i | \(0.537067\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 6.00000 | + | 10.3923i | 0.278243 | + | 0.481932i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 4.00000 | − | 6.92820i | 0.185098 | − | 0.320599i | −0.758512 | − | 0.651660i | \(-0.774073\pi\) |
0.943610 | + | 0.331061i | \(0.107406\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −14.0000 | − | 12.1244i | −0.646460 | − | 0.559851i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.00000 | − | 8.66025i | 0.230388 | − | 0.399043i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −15.0000 | − | 25.9808i | −0.689701 | − | 1.19460i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −11.0000 | −0.504715 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 6.00000 | 0.274721 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.00000 | − | 1.73205i | −0.0456912 | − | 0.0791394i | 0.842275 | − | 0.539048i | \(-0.181216\pi\) |
−0.887967 | + | 0.459908i | \(0.847882\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.50000 | + | 12.9904i | −0.341971 | + | 0.592310i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 15.0000 | − | 5.19615i | 0.682524 | − | 0.236433i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 12.0000 | − | 20.7846i | 0.544892 | − | 0.943781i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0.500000 | + | 0.866025i | 0.0226572 | + | 0.0392434i | 0.877132 | − | 0.480250i | \(-0.159454\pi\) |
−0.854475 | + | 0.519493i | \(0.826121\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −20.0000 | −0.904431 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8.00000 | −0.361035 | −0.180517 | − | 0.983572i | \(-0.557777\pi\) | ||||
−0.180517 | + | 0.983572i | \(0.557777\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 12.0000 | − | 20.7846i | 0.539360 | − | 0.934199i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −40.0000 | + | 13.8564i | −1.79425 | + | 0.621545i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14.5000 | − | 25.1147i | 0.649109 | − | 1.12429i | −0.334227 | − | 0.942493i | \(-0.608475\pi\) |
0.983336 | − | 0.181797i | \(-0.0581915\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4.00000 | + | 6.92820i | 0.178707 | + | 0.309529i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 18.0000 | 0.802580 | 0.401290 | − | 0.915951i | \(-0.368562\pi\) | ||||
0.401290 | + | 0.915951i | \(0.368562\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −8.00000 | −0.355995 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −6.00000 | − | 10.3923i | −0.266469 | − | 0.461538i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −12.0000 | + | 20.7846i | −0.531891 | + | 0.921262i | 0.467416 | + | 0.884037i | \(0.345185\pi\) |
−0.999307 | + | 0.0372243i | \(0.988148\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.00000 | − | 5.19615i | −0.265424 | − | 0.229864i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.500000 | − | 0.866025i | 0.0220755 | − | 0.0382360i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 22.0000 | + | 38.1051i | 0.969436 | + | 1.67911i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 24.0000 | 1.05552 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −22.0000 | −0.965693 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −12.0000 | − | 20.7846i | −0.525730 | − | 0.910590i | −0.999551 | − | 0.0299693i | \(-0.990459\pi\) |
0.473821 | − | 0.880621i | \(-0.342874\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8.50000 | + | 14.7224i | −0.371679 | + | 0.643767i | −0.989824 | − | 0.142297i | \(-0.954551\pi\) |
0.618145 | + | 0.786064i | \(0.287884\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 5.50000 | − | 28.5788i | 0.240040 | − | 1.24728i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.00000 | − | 5.19615i | 0.130682 | − | 0.226348i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.50000 | − | 11.2583i | −0.282609 | − | 0.489493i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6.00000 | 0.260378 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 30.0000 | 1.29944 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 20.0000 | + | 34.6410i | 0.864675 | + | 1.49766i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 39.0000 | + | 15.5885i | 1.67985 | + | 0.671442i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18.5000 | − | 32.0429i | 0.795377 | − | 1.37763i | −0.127222 | − | 0.991874i | \(-0.540606\pi\) |
0.922599 | − | 0.385759i | \(-0.126061\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 12.5000 | + | 21.6506i | 0.536426 | + | 0.929118i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 60.0000 | 2.57012 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −28.0000 | −1.19719 | −0.598597 | − | 0.801050i | \(-0.704275\pi\) | ||||
−0.598597 | + | 0.801050i | \(0.704275\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.00000 | − | 1.73205i | −0.0426790 | − | 0.0739221i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.50000 | − | 28.5788i | 0.233884 | − | 1.21530i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 6.00000 | − | 10.3923i | 0.254686 | − | 0.441129i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −3.00000 | − | 5.19615i | −0.127114 | − | 0.220168i | 0.795443 | − | 0.606028i | \(-0.207238\pi\) |
−0.922557 | + | 0.385860i | \(0.873905\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 25.0000 | 1.05739 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −12.0000 | −0.506640 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 12.0000 | + | 20.7846i | 0.505740 | + | 0.875967i | 0.999978 | + | 0.00664037i | \(0.00211371\pi\) |
−0.494238 | + | 0.869326i | \(0.664553\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 32.0000 | − | 55.4256i | 1.34625 | − | 2.33177i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.00000 | + | 1.73205i | 0.0839921 | + | 0.0727393i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −9.00000 | + | 15.5885i | −0.377300 | + | 0.653502i | −0.990668 | − | 0.136295i | \(-0.956481\pi\) |
0.613369 | + | 0.789797i | \(0.289814\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14.5000 | + | 25.1147i | 0.606806 | + | 1.05102i | 0.991763 | + | 0.128085i | \(0.0408829\pi\) |
−0.384957 | + | 0.922934i | \(0.625784\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −66.0000 | −2.75239 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −11.5000 | − | 19.9186i | −0.478751 | − | 0.829222i | 0.520952 | − | 0.853586i | \(-0.325577\pi\) |
−0.999703 | + | 0.0243645i | \(0.992244\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0.500000 | − | 0.866025i | 0.0207793 | − | 0.0359908i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 30.0000 | − | 10.3923i | 1.24461 | − | 0.431145i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 18.0000 | − | 31.1769i | 0.745484 | − | 1.29122i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 10.0000 | + | 17.3205i | 0.413449 | + | 0.716115i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −40.0000 | −1.65098 | −0.825488 | − | 0.564419i | \(-0.809100\pi\) | ||||
−0.825488 | + | 0.564419i | \(0.809100\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.00000 | 0.123613 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 9.00000 | + | 15.5885i | 0.370211 | + | 0.641223i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 13.0000 | − | 22.5167i | 0.533846 | − | 0.924648i | −0.465372 | − | 0.885115i | \(-0.654080\pi\) |
0.999218 | − | 0.0395334i | \(-0.0125871\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −20.0000 | + | 6.92820i | −0.819920 | + | 0.284029i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −10.0000 | + | 17.3205i | −0.409273 | + | 0.708881i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −10.0000 | − | 17.3205i | −0.408589 | − | 0.707697i | 0.586143 | − | 0.810208i | \(-0.300646\pi\) |
−0.994732 | + | 0.102511i | \(0.967312\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −21.0000 | −0.856608 | −0.428304 | − | 0.903635i | \(-0.640889\pi\) | ||||
−0.428304 | + | 0.903635i | \(0.640889\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −7.00000 | −0.285062 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −50.0000 | − | 86.6025i | −2.03279 | − | 3.52089i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.50000 | − | 4.33013i | 0.101472 | − | 0.175754i | −0.810819 | − | 0.585296i | \(-0.800978\pi\) |
0.912291 | + | 0.409542i | \(0.134311\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −10.0000 | + | 17.3205i | −0.404557 | + | 0.700713i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −23.0000 | − | 39.8372i | −0.928961 | − | 1.60901i | −0.785063 | − | 0.619416i | \(-0.787370\pi\) |
−0.143898 | − | 0.989593i | \(-0.545964\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −24.0000 | −0.967773 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −14.0000 | −0.563619 | −0.281809 | − | 0.959470i | \(-0.590935\pi\) | ||||
−0.281809 | + | 0.959470i | \(0.590935\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −12.5000 | − | 21.6506i | −0.502417 | − | 0.870212i | −0.999996 | − | 0.00279365i | \(-0.999111\pi\) |
0.497579 | − | 0.867419i | \(-0.334223\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.00000 | − | 5.19615i | 0.120386 | − | 0.208514i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.00000 | − | 10.3923i | 0.0801283 | − | 0.416359i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −20.5000 | + | 35.5070i | −0.820000 | + | 1.42028i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3.00000 | − | 5.19615i | −0.119808 | − | 0.207514i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −6.00000 | −0.239236 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 28.0000 | 1.11466 | 0.557331 | − | 0.830290i | \(-0.311825\pi\) | ||||
0.557331 | + | 0.830290i | \(0.311825\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 6.00000 | + | 10.3923i | 0.238479 | + | 0.413057i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 14.0000 | − | 24.2487i | 0.555573 | − | 0.962281i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −27.5000 | + | 21.6506i | −1.08959 | + | 0.857829i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −8.00000 | + | 13.8564i | −0.316475 | + | 0.548151i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −19.0000 | − | 32.9090i | −0.750455 | − | 1.29983i | −0.947602 | − | 0.319452i | \(-0.896501\pi\) |
0.197148 | − | 0.980374i | \(-0.436832\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 23.0000 | 0.907031 | 0.453516 | − | 0.891248i | \(-0.350170\pi\) | ||||
0.453516 | + | 0.891248i | \(0.350170\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −20.0000 | −0.787499 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −5.00000 | − | 8.66025i | −0.196570 | − | 0.340470i | 0.750844 | − | 0.660480i | \(-0.229647\pi\) |
−0.947414 | + | 0.320010i | \(0.896314\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 18.0000 | − | 31.1769i | 0.706562 | − | 1.22380i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.50000 | + | 7.79423i | −0.0587896 | + | 0.305480i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 17.0000 | − | 29.4449i | 0.665261 | − | 1.15227i | −0.313953 | − | 0.949439i | \(-0.601653\pi\) |
0.979214 | − | 0.202828i | \(-0.0650132\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 12.0000 | + | 20.7846i | 0.468879 | + | 0.812122i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −3.00000 | −0.117041 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −6.00000 | −0.233727 | −0.116863 | − | 0.993148i | \(-0.537284\pi\) | ||||
−0.116863 | + | 0.993148i | \(0.537284\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.50000 | + | 2.59808i | 0.0583432 | + | 0.101053i | 0.893722 | − | 0.448622i | \(-0.148085\pi\) |
−0.835379 | + | 0.549675i | \(0.814752\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 5.00000 | − | 8.66025i | 0.194184 | − | 0.336336i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −8.00000 | − | 6.92820i | −0.310227 | − | 0.268664i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −8.00000 | − | 13.8564i | −0.309298 | − | 0.535720i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −12.0000 | −0.463255 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −29.0000 | −1.11787 | −0.558934 | − | 0.829212i | \(-0.688789\pi\) | ||||
−0.558934 | + | 0.829212i | \(0.688789\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −5.50000 | − | 9.52628i | −0.211695 | − | 0.366667i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −6.00000 | + | 10.3923i | −0.230599 | + | 0.399409i | −0.957984 | − | 0.286820i | \(-0.907402\pi\) |
0.727386 | + | 0.686229i | \(0.240735\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 15.0000 | − | 5.19615i | 0.575647 | − | 0.199410i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 11.0000 | − | 19.0526i | 0.421521 | − | 0.730096i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 9.00000 | + | 15.5885i | 0.344375 | + | 0.596476i | 0.985240 | − | 0.171178i | \(-0.0547574\pi\) |
−0.640865 | + | 0.767654i | \(0.721424\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −48.0000 | −1.83399 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 11.0000 | 0.419676 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 15.0000 | + | 25.9808i | 0.571454 | + | 0.989788i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 11.5000 | − | 19.9186i | 0.437481 | − | 0.757739i | −0.560014 | − | 0.828483i | \(-0.689204\pi\) |
0.997494 | + | 0.0707446i | \(0.0225375\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 15.0000 | − | 5.19615i | 0.569803 | − | 0.197386i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 10.0000 | − | 17.3205i | 0.379322 | − | 0.657004i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.00000 | + | 10.3923i | 0.227266 | + | 0.393637i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −8.00000 | −0.302588 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −22.0000 | −0.830929 | −0.415464 | − | 0.909610i | \(-0.636381\pi\) | ||||
−0.415464 | + | 0.909610i | \(0.636381\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.50000 | − | 2.59808i | −0.0565736 | − | 0.0979883i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 8.00000 | − | 13.8564i | 0.301297 | − | 0.521862i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −4.00000 | − | 3.46410i | −0.150435 | − | 0.130281i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.00000 | + | 5.19615i | −0.112667 | + | 0.195146i | −0.916845 | − | 0.399244i | \(-0.869273\pi\) |
0.804178 | + | 0.594389i | \(0.202606\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.50000 | − | 9.52628i | −0.206266 | − | 0.357263i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 18.0000 | 0.674105 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 120.000 | 4.48775 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.00000 | − | 1.73205i | −0.0373457 | − | 0.0646846i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −15.0000 | + | 25.9808i | −0.559406 | + | 0.968919i | 0.438141 | + | 0.898906i | \(0.355637\pi\) |
−0.997546 | + | 0.0700124i | \(0.977696\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.50000 | + | 28.5788i | −0.204831 | + | 1.06433i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −5.00000 | + | 8.66025i | −0.185952 | + | 0.322078i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −41.0000 | −1.52061 | −0.760303 | − | 0.649569i | \(-0.774949\pi\) | ||||
−0.760303 | + | 0.649569i | \(0.774949\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.00000 | + | 8.66025i | 0.184932 | + | 0.320311i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 10.5000 | − | 18.1865i | 0.387826 | − | 0.671735i | −0.604331 | − | 0.796734i | \(-0.706559\pi\) |
0.992157 | + | 0.124999i | \(0.0398927\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 22.0000 | − | 17.3205i | 0.811482 | − | 0.638877i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −21.0000 | + | 36.3731i | −0.773545 | + | 1.33982i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −25.5000 | − | 44.1673i | −0.938033 | − | 1.62472i | −0.769135 | − | 0.639087i | \(-0.779313\pi\) |
−0.168898 | − | 0.985634i | \(-0.554021\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5.00000 | 0.183680 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −18.0000 | −0.660356 | −0.330178 | − | 0.943919i | \(-0.607109\pi\) | ||||
−0.330178 | + | 0.943919i | \(0.607109\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −8.00000 | − | 13.8564i | −0.293097 | − | 0.507659i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 6.00000 | − | 10.3923i | 0.219529 | − | 0.380235i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −5.00000 | + | 25.9808i | −0.182696 | + | 0.949316i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.50000 | − | 6.06218i | 0.127717 | − | 0.221212i | −0.795075 | − | 0.606511i | \(-0.792568\pi\) |
0.922792 | + | 0.385299i | \(0.125902\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −7.00000 | − | 12.1244i | −0.255094 | − | 0.441836i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −32.0000 | −1.16460 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 26.0000 | 0.944986 | 0.472493 | − | 0.881334i | \(-0.343354\pi\) | ||||
0.472493 | + | 0.881334i | \(0.343354\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −18.0000 | − | 31.1769i | −0.653359 | − | 1.13165i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −25.0000 | + | 43.3013i | −0.906249 | + | 1.56967i | −0.0870179 | + | 0.996207i | \(0.527734\pi\) |
−0.819231 | + | 0.573463i | \(0.805600\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 30.0000 | + | 25.9808i | 1.08607 | + | 0.940567i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4.00000 | + | 6.92820i | −0.144620 | + | 0.250490i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 15.0000 | + | 25.9808i | 0.541619 | + | 0.938111i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 31.0000 | 1.11789 | 0.558944 | − | 0.829205i | \(-0.311207\pi\) | ||||
0.558944 | + | 0.829205i | \(0.311207\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −12.0000 | −0.432169 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −11.0000 | − | 19.0526i | −0.395643 | − | 0.685273i | 0.597540 | − | 0.801839i | \(-0.296145\pi\) |
−0.993183 | + | 0.116566i | \(0.962811\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 16.5000 | − | 28.5788i | 0.592697 | − | 1.02658i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 7.50000 | − | 2.59808i | 0.269061 | − | 0.0932055i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.00000 | + | 5.19615i | −0.107486 | + | 0.186171i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 48.0000 | + | 83.1384i | 1.71758 | + | 2.97493i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −40.0000 | −1.42766 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 16.0000 | + | 27.7128i | 0.570338 | + | 0.987855i | 0.996531 | + | 0.0832226i | \(0.0265213\pi\) |
−0.426193 | + | 0.904632i | \(0.640145\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 40.0000 | − | 13.8564i | 1.42224 | − | 0.492677i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.00000 | − | 8.66025i | 0.177555 | − | 0.307535i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −12.0000 | − | 20.7846i | −0.425596 | − | 0.737154i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 46.0000 | 1.62940 | 0.814702 | − | 0.579880i | \(-0.196901\pi\) | ||||
0.814702 | + | 0.579880i | \(0.196901\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8.00000 | −0.283020 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.00000 | − | 3.46410i | −0.0706665 | − | 0.122398i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −9.00000 | + | 15.5885i | −0.317603 | + | 0.550105i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −48.0000 | − | 41.5692i | −1.69178 | − | 1.46512i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.00000 | + | 1.73205i | −0.0352017 | + | 0.0609711i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −4.00000 | − | 6.92820i | −0.140633 | − | 0.243583i | 0.787102 | − | 0.616822i | \(-0.211580\pi\) |
−0.927735 | + | 0.373240i | \(0.878247\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −28.0000 | −0.983213 | −0.491606 | − | 0.870817i | \(-0.663590\pi\) | ||||
−0.491606 | + | 0.870817i | \(0.663590\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 16.0000 | 0.561144 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 40.0000 | + | 69.2820i | 1.40114 | + | 2.42684i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.50000 | + | 4.33013i | −0.0874639 | + | 0.151492i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.50000 | + | 12.9904i | −0.0873571 | + | 0.453921i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.00000 | − | 3.46410i | 0.0698005 | − | 0.120898i | −0.829013 | − | 0.559229i | \(-0.811097\pi\) |
0.898813 | + | 0.438331i | \(0.144430\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 12.0000 | + | 20.7846i | 0.418294 | + | 0.724506i | 0.995768 | − | 0.0919029i | \(-0.0292950\pi\) |
−0.577474 | + | 0.816409i | \(0.695962\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −66.0000 | −2.29783 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −12.0000 | −0.417281 | −0.208640 | − | 0.977992i | \(-0.566904\pi\) | ||||
−0.208640 | + | 0.977992i | \(0.566904\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.50000 | + | 4.33013i | 0.0868286 | + | 0.150392i | 0.906169 | − | 0.422916i | \(-0.138993\pi\) |
−0.819340 | + | 0.573307i | \(0.805660\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0.500000 | − | 0.866025i | 0.0173448 | − | 0.0300421i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −13.0000 | − | 5.19615i | −0.450423 | − | 0.180036i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 16.0000 | − | 27.7128i | 0.553703 | − | 0.959041i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.50000 | + | 2.59808i | 0.0518476 | + | 0.0898027i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 12.0000 | 0.414286 | 0.207143 | − | 0.978311i | \(-0.433583\pi\) | ||||
0.207143 | + | 0.978311i | \(0.433583\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −29.0000 | −1.00000 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −3.00000 | − | 5.19615i | −0.103325 | − | 0.178965i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −24.0000 | + | 41.5692i | −0.825625 | + | 1.43002i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 12.5000 | − | 64.9519i | 0.429505 | − | 2.23177i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −5.50000 | + | 9.52628i | −0.188760 | + | 0.326941i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −9.00000 | − | 15.5885i | −0.308516 | − | 0.534365i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 33.0000 | 1.12990 | 0.564949 | − | 0.825126i | \(-0.308896\pi\) | ||||
0.564949 | + | 0.825126i | \(0.308896\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4.00000 | −0.136797 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −12.0000 | − | 20.7846i | −0.409912 | − | 0.709989i | 0.584967 | − | 0.811057i | \(-0.301107\pi\) |
−0.994880 | + | 0.101068i | \(0.967774\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 26.0000 | − | 45.0333i | 0.887109 | − | 1.53652i | 0.0438309 | − | 0.999039i | \(-0.486044\pi\) |
0.843278 | − | 0.537478i | \(-0.180623\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −12.0000 | − | 10.3923i | −0.408959 | − | 0.354169i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −27.0000 | + | 46.7654i | −0.919091 | + | 1.59191i | −0.118291 | + | 0.992979i | \(0.537742\pi\) |
−0.800799 | + | 0.598933i | \(0.795592\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 44.0000 | + | 76.2102i | 1.49604 | + | 2.59123i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −13.0000 | −0.441503 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −66.0000 | −2.23890 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −17.5000 | − | 30.3109i | −0.592965 | − | 1.02705i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3.00000 | − | 5.19615i | 0.101535 | − | 0.175863i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −60.0000 | + | 20.7846i | −2.02837 | + | 0.702648i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.00000 | − | 1.73205i | 0.0337676 | − | 0.0584872i | −0.848648 | − | 0.528958i | \(-0.822583\pi\) |
0.882415 | + | 0.470471i | \(0.155916\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −6.00000 | − | 10.3923i | −0.202375 | − | 0.350524i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −42.0000 | −1.41502 | −0.707508 | − | 0.706705i | \(-0.750181\pi\) | ||||
−0.707508 | + | 0.706705i | \(0.750181\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −7.00000 | −0.235569 | −0.117784 | − | 0.993039i | \(-0.537579\pi\) | ||||
−0.117784 | + | 0.993039i | \(0.537579\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −12.0000 | − | 20.7846i | −0.403376 | − | 0.698667i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −17.0000 | + | 29.4449i | −0.570804 | + | 0.988662i | 0.425679 | + | 0.904874i | \(0.360035\pi\) |
−0.996484 | + | 0.0837878i | \(0.973298\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 17.5000 | − | 6.06218i | 0.586931 | − | 0.203319i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.00000 | − | 5.19615i | 0.100504 | − | 0.174078i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.00000 | − | 3.46410i | −0.0669274 | − | 0.115922i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 30.0000 | 1.00167 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.00000 | + | 10.3923i | −0.199889 | + | 0.346218i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −10.0000 | − | 8.66025i | −0.332779 | − | 0.288195i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 50.0000 | − | 86.6025i | 1.66206 | − | 2.87877i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 21.5000 | + | 37.2391i | 0.713896 | + | 1.23650i | 0.963384 | + | 0.268126i | \(0.0864043\pi\) |
−0.249488 | + | 0.968378i | \(0.580262\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −2.00000 | −0.0663358 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −26.0000 | −0.861418 | −0.430709 | − | 0.902491i | \(-0.641737\pi\) | ||||
−0.430709 | + | 0.902491i | \(0.641737\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −36.0000 | − | 62.3538i | −1.19143 | − | 2.06361i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −4.00000 | + | 6.92820i | −0.132236 | + | 0.229039i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −3.00000 | + | 15.5885i | −0.0990687 | + | 0.514776i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −21.5000 | + | 37.2391i | −0.709220 | + | 1.22840i | 0.255927 | + | 0.966696i | \(0.417619\pi\) |
−0.965147 | + | 0.261708i | \(0.915714\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 5.50000 | + | 9.52628i | 0.181231 | + | 0.313902i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −80.0000 | −2.63323 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −33.0000 | −1.08503 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 5.50000 | + | 9.52628i | 0.180644 | + | 0.312884i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 18.0000 | − | 31.1769i | 0.590561 | − | 1.02288i | −0.403596 | − | 0.914937i | \(-0.632240\pi\) |
0.994157 | − | 0.107944i | \(-0.0344268\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.00000 | − | 6.92820i | −0.0327737 | − | 0.227063i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.00000 | − | 1.73205i | 0.0327385 | − | 0.0567048i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 24.0000 | + | 41.5692i | 0.784884 | + | 1.35946i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 51.0000 | 1.66610 | 0.833049 | − | 0.553200i | \(-0.186593\pi\) | ||||
0.833049 | + | 0.553200i | \(0.186593\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 31.0000 | 1.01165 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 27.0000 | + | 46.7654i | 0.880175 | + | 1.52451i | 0.851146 | + | 0.524929i | \(0.175908\pi\) |
0.0290288 | + | 0.999579i | \(0.490759\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −18.0000 | + | 31.1769i | −0.586161 | + | 1.01526i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.00000 | − | 10.3923i | 0.0650600 | − | 0.338062i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −15.0000 | + | 25.9808i | −0.487435 | + | 0.844261i | −0.999896 | − | 0.0144491i | \(-0.995401\pi\) |
0.512461 | + | 0.858710i | \(0.328734\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −7.50000 | − | 12.9904i | −0.243460 | − | 0.421686i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 20.0000 | 0.648544 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −6.00000 | −0.194359 | −0.0971795 | − | 0.995267i | \(-0.530982\pi\) | ||||
−0.0971795 | + | 0.995267i | \(0.530982\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −24.0000 | − | 20.7846i | −0.775000 | − | 0.671170i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 11.0000 | − | 19.0526i | 0.354839 | − | 0.614599i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 5.00000 | + | 8.66025i | 0.161123 | + | 0.279073i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −4.00000 | −0.128765 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −53.0000 | −1.70437 | −0.852183 | − | 0.523245i | \(-0.824721\pi\) | ||||
−0.852183 | + | 0.523245i | \(0.824721\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.00000 | + | 1.73205i | 0.0321246 | + | 0.0556415i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −13.0000 | + | 22.5167i | −0.417190 | + | 0.722594i | −0.995656 | − | 0.0931127i | \(-0.970318\pi\) |
0.578466 | + | 0.815707i | \(0.303652\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 12.5000 | − | 4.33013i | 0.400732 | − | 0.138817i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 27.5000 | − | 47.6314i | 0.880705 | − | 1.52543i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −15.0000 | − | 25.9808i | −0.479893 | − | 0.831198i | 0.519841 | − | 0.854263i | \(-0.325991\pi\) |
−0.999734 | + | 0.0230645i | \(0.992658\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −24.0000 | −0.767043 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 15.0000 | 0.478913 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −13.0000 | − | 22.5167i | −0.414636 | − | 0.718170i | 0.580755 | − | 0.814079i | \(-0.302758\pi\) |
−0.995390 | + | 0.0959088i | \(0.969424\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 36.0000 | − | 62.3538i | 1.14706 | − | 1.98676i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 10.0000 | − | 3.46410i | 0.318304 | − | 0.110264i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −15.0000 | + | 25.9808i | −0.476972 | + | 0.826140i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −12.5000 | − | 21.6506i | −0.397076 | − | 0.687755i | 0.596288 | − | 0.802771i | \(-0.296642\pi\) |
−0.993364 | + | 0.115015i | \(0.963308\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 5.00000 | 0.158670 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 80.0000 | 2.53617 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.50000 | − | 4.33013i | −0.0791758 | − | 0.137136i | 0.823719 | − | 0.566999i | \(-0.191896\pi\) |
−0.902895 | + | 0.429862i | \(0.858562\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.50000 | − | 2.59808i | 0.0474579 | − | 0.0821995i |
(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 | 1344.2.q.a.961.1 | 2 | ||
4.3 | odd | 2 | 1344.2.q.l.961.1 | 2 | |||
7.2 | even | 3 | 9408.2.a.dd.1.1 | 1 | |||
7.4 | even | 3 | inner | 1344.2.q.a.193.1 | 2 | ||
7.5 | odd | 6 | 9408.2.a.a.1.1 | 1 | |||
8.3 | odd | 2 | 672.2.q.e.289.1 | yes | 2 | ||
8.5 | even | 2 | 672.2.q.j.289.1 | yes | 2 | ||
24.5 | odd | 2 | 2016.2.s.a.289.1 | 2 | |||
24.11 | even | 2 | 2016.2.s.b.289.1 | 2 | |||
28.11 | odd | 6 | 1344.2.q.l.193.1 | 2 | |||
28.19 | even | 6 | 9408.2.a.bs.1.1 | 1 | |||
28.23 | odd | 6 | 9408.2.a.bp.1.1 | 1 | |||
56.5 | odd | 6 | 4704.2.a.bh.1.1 | 1 | |||
56.11 | odd | 6 | 672.2.q.e.193.1 | ✓ | 2 | ||
56.19 | even | 6 | 4704.2.a.p.1.1 | 1 | |||
56.37 | even | 6 | 4704.2.a.a.1.1 | 1 | |||
56.51 | odd | 6 | 4704.2.a.r.1.1 | 1 | |||
56.53 | even | 6 | 672.2.q.j.193.1 | yes | 2 | ||
168.11 | even | 6 | 2016.2.s.b.865.1 | 2 | |||
168.53 | odd | 6 | 2016.2.s.a.865.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
672.2.q.e.193.1 | ✓ | 2 | 56.11 | odd | 6 | ||
672.2.q.e.289.1 | yes | 2 | 8.3 | odd | 2 | ||
672.2.q.j.193.1 | yes | 2 | 56.53 | even | 6 | ||
672.2.q.j.289.1 | yes | 2 | 8.5 | even | 2 | ||
1344.2.q.a.193.1 | 2 | 7.4 | even | 3 | inner | ||
1344.2.q.a.961.1 | 2 | 1.1 | even | 1 | trivial | ||
1344.2.q.l.193.1 | 2 | 28.11 | odd | 6 | |||
1344.2.q.l.961.1 | 2 | 4.3 | odd | 2 | |||
2016.2.s.a.289.1 | 2 | 24.5 | odd | 2 | |||
2016.2.s.a.865.1 | 2 | 168.53 | odd | 6 | |||
2016.2.s.b.289.1 | 2 | 24.11 | even | 2 | |||
2016.2.s.b.865.1 | 2 | 168.11 | even | 6 | |||
4704.2.a.a.1.1 | 1 | 56.37 | even | 6 | |||
4704.2.a.p.1.1 | 1 | 56.19 | even | 6 | |||
4704.2.a.r.1.1 | 1 | 56.51 | odd | 6 | |||
4704.2.a.bh.1.1 | 1 | 56.5 | odd | 6 | |||
9408.2.a.a.1.1 | 1 | 7.5 | odd | 6 | |||
9408.2.a.bp.1.1 | 1 | 28.23 | odd | 6 | |||
9408.2.a.bs.1.1 | 1 | 28.19 | even | 6 | |||
9408.2.a.dd.1.1 | 1 | 7.2 | even | 3 |