Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [260,2,Mod(3,260)]
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, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("260.3");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 260 = 2^{2} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 260.bj (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 | 243.1 | ||
Root | \(0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 260.243 |
Dual form | 260.2.bj.a.107.1 |
$q$-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 \(\left(\mathbb{Z}/260\mathbb{Z}\right)^\times\).
\(n\) | \(41\) | \(131\) | \(157\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.366025 | − | 1.36603i | −0.258819 | − | 0.965926i | ||||
\(3\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(4\) | −1.73205 | + | 1.00000i | −0.866025 | + | 0.500000i | ||||
\(5\) | 1.86603 | − | 1.23205i | 0.834512 | − | 0.550990i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(8\) | 2.00000 | + | 2.00000i | 0.707107 | + | 0.707107i | ||||
\(9\) | 2.59808 | − | 1.50000i | 0.866025 | − | 0.500000i | ||||
\(10\) | −2.36603 | − | 2.09808i | −0.748203 | − | 0.663470i | ||||
\(11\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.232051 | − | 3.59808i | −0.0643593 | − | 0.997927i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.00000 | − | 3.46410i | 0.500000 | − | 0.866025i | ||||
\(17\) | −3.86603 | − | 1.03590i | −0.937649 | − | 0.251242i | −0.242536 | − | 0.970143i | \(-0.577979\pi\) |
−0.695113 | + | 0.718900i | \(0.744646\pi\) | |||||||
\(18\) | −3.00000 | − | 3.00000i | −0.707107 | − | 0.707107i | ||||
\(19\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(20\) | −2.00000 | + | 4.00000i | −0.447214 | + | 0.894427i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.96410 | − | 4.59808i | 0.392820 | − | 0.919615i | ||||
\(26\) | −4.83013 | + | 1.63397i | −0.947266 | + | 0.320449i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.76795 | + | 3.33013i | 1.07108 | + | 0.618389i | 0.928477 | − | 0.371391i | \(-0.121119\pi\) |
0.142605 | + | 0.989780i | \(0.454452\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(32\) | −5.46410 | − | 1.46410i | −0.965926 | − | 0.258819i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 5.66025i | 0.970726i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −3.00000 | + | 5.19615i | −0.500000 | + | 0.866025i | ||||
\(37\) | −0.303848 | − | 1.13397i | −0.0499522 | − | 0.186424i | 0.936442 | − | 0.350823i | \(-0.114098\pi\) |
−0.986394 | + | 0.164399i | \(0.947432\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 6.19615 | + | 1.26795i | 0.979698 | + | 0.200480i | ||||
\(41\) | −6.33013 | + | 10.9641i | −0.988600 | + | 1.71230i | −0.363905 | + | 0.931436i | \(0.618557\pi\) |
−0.624695 | + | 0.780869i | \(0.714777\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(44\) | 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 | ||||
\(53\) | −0.169873 | − | 0.169873i | −0.0233338 | − | 0.0233338i | 0.695344 | − | 0.718677i | \(-0.255252\pi\) |
−0.718677 | + | 0.695344i | \(0.755252\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.43782 | − | 9.09808i | 0.320102 | − | 1.19464i | ||||
\(59\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.33013 | + | 12.6962i | 0.938527 | + | 1.62558i | 0.768221 | + | 0.640184i | \(0.221142\pi\) |
0.170305 | + | 0.985391i | \(0.445525\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.00000i | 1.00000i | ||||||||
\(65\) | −4.86603 | − | 6.42820i | −0.603556 | − | 0.797320i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(68\) | 7.73205 | − | 2.07180i | 0.937649 | − | 0.251242i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(72\) | 8.19615 | + | 2.19615i | 0.965926 | + | 0.258819i | ||||
\(73\) | 9.83013 | + | 9.83013i | 1.15053 | + | 1.15053i | 0.986447 | + | 0.164083i | \(0.0524664\pi\) |
0.164083 | + | 0.986447i | \(0.447534\pi\) | |||||||
\(74\) | −1.43782 | + | 0.830127i | −0.167143 | + | 0.0965003i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(80\) | −0.535898 | − | 8.92820i | −0.0599153 | − | 0.998203i | ||||
\(81\) | 4.50000 | − | 7.79423i | 0.500000 | − | 0.866025i | ||||
\(82\) | 17.2942 | + | 4.63397i | 1.90983 | + | 0.511737i | ||||
\(83\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −8.49038 | + | 2.83013i | −0.920911 | + | 0.306970i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −13.8564 | − | 8.00000i | −1.46878 | − | 0.847998i | −0.469389 | − | 0.882992i | \(-0.655526\pi\) |
−0.999388 | + | 0.0349934i | \(0.988859\pi\) | |||||||
\(90\) | −9.29423 | − | 1.90192i | −0.979698 | − | 0.200480i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −17.7583 | − | 4.75833i | −1.80309 | − | 0.483135i | −0.808632 | − | 0.588315i | \(-0.799792\pi\) |
−0.994453 | + | 0.105180i | \(0.966458\pi\) | |||||||
\(98\) | 2.56218 | − | 9.56218i | 0.258819 | − | 0.965926i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.19615 | + | 9.92820i | 0.119615 | + | 0.992820i | ||||
\(101\) | −8.16025 | + | 14.1340i | −0.811976 | + | 1.40638i | 0.0995037 | + | 0.995037i | \(0.468274\pi\) |
−0.911479 | + | 0.411346i | \(0.865059\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(104\) | 6.73205 | − | 7.66025i | 0.660132 | − | 0.751150i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.169873 | + | 0.294229i | −0.0164995 | + | 0.0285780i | ||||
\(107\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.00000i | 0.574696i | 0.957826 | + | 0.287348i | \(0.0927736\pi\) | ||||
−0.957826 | + | 0.287348i | \(0.907226\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.57180 | + | 17.0622i | −0.430078 | + | 1.60507i | 0.322498 | + | 0.946570i | \(0.395477\pi\) |
−0.752577 | + | 0.658505i | \(0.771189\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −13.3205 | −1.23678 | ||||||||
\(117\) | −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 | ||||
\(122\) | 14.6603 | − | 14.6603i | 1.32728 | − | 1.32728i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −2.00000 | − | 11.0000i | −0.178885 | − | 0.983870i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(128\) | 10.9282 | − | 2.92820i | 0.965926 | − | 0.258819i | ||||
\(129\) | 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 | ||||||||
\(136\) | −5.66025 | − | 9.80385i | −0.485363 | − | 0.840673i | ||||
\(137\) | −22.5263 | − | 6.03590i | −1.92455 | − | 0.515682i | −0.984757 | − | 0.173939i | \(-0.944351\pi\) |
−0.939793 | − | 0.341743i | \(-0.888983\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | − | 12.0000i | − | 1.00000i | ||||||
\(145\) | 14.8660 | − | 0.892305i | 1.23456 | − | 0.0741019i | ||||
\(146\) | 9.83013 | − | 17.0263i | 0.813547 | − | 1.40910i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.66025 | + | 1.66025i | 0.136472 | + | 0.136472i | ||||
\(149\) | 21.0622 | − | 12.1603i | 1.72548 | − | 0.996207i | 0.819232 | − | 0.573462i | \(-0.194400\pi\) |
0.906249 | − | 0.422744i | \(-0.138933\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −11.5981 | + | 3.10770i | −0.937649 | + | 0.251242i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.8301 | − | 12.8301i | 1.02396 | − | 1.02396i | 0.0242497 | − | 0.999706i | \(-0.492280\pi\) |
0.999706 | − | 0.0242497i | \(-0.00771967\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −12.0000 | + | 4.00000i | −0.948683 | + | 0.316228i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −12.2942 | − | 3.29423i | −0.965926 | − | 0.258819i | ||||
\(163\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(164\) | − | 25.3205i | − | 1.97720i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.8923 | + | 1.66987i | −0.991716 | + | 0.128452i | ||||
\(170\) | 6.97372 | + | 10.5622i | 0.534860 | + | 0.810082i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4.02628 | + | 15.0263i | −0.306112 | + | 1.14243i | 0.625871 | + | 0.779926i | \(0.284744\pi\) |
−0.931984 | + | 0.362500i | \(0.881923\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −5.85641 | + | 21.8564i | −0.438956 | + | 1.63821i | ||||
\(179\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(180\) | 0.803848 | + | 13.3923i | 0.0599153 | + | 0.998203i | ||||
\(181\) | 26.3205 | 1.95639 | 0.978194 | − | 0.207693i | \(-0.0665956\pi\) | ||||
0.978194 | + | 0.207693i | \(0.0665956\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.96410 | − | 1.74167i | −0.144404 | − | 0.128050i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 18.8923 | − | 5.06218i | 1.35990 | − | 0.364384i | 0.496119 | − | 0.868255i | \(-0.334758\pi\) |
0.863779 | + | 0.503871i | \(0.168091\pi\) | |||||||
\(194\) | 26.0000i | 1.86669i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −14.0000 | −1.00000 | ||||||||
\(197\) | 4.75833 | + | 17.7583i | 0.339017 | + | 1.26523i | 0.899448 | + | 0.437028i | \(0.143969\pi\) |
−0.560431 | + | 0.828201i | \(0.689365\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(200\) | 13.1244 | − | 5.26795i | 0.928032 | − | 0.372500i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 22.2942 | + | 5.97372i | 1.56862 | + | 0.420310i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.69615 | + | 28.2583i | 0.118464 | + | 1.97365i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −12.9282 | − | 6.39230i | −0.896410 | − | 0.443227i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(212\) | 0.464102 | + | 0.124356i | 0.0318746 | + | 0.00854078i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 8.19615 | − | 2.19615i | 0.555113 | − | 0.148742i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.83013 | + | 14.1506i | −0.190375 | + | 0.951875i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.79423 | − | 14.8923i | −0.119615 | − | 0.992820i | ||||
\(226\) | 24.9808 | 1.66170 | ||||||||
\(227\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 4.00000i | − | 0.264327i | −0.991228 | − | 0.132164i | \(-0.957808\pi\) | ||
0.991228 | − | 0.132164i | \(-0.0421925\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.87564 | + | 18.1962i | 0.320102 | + | 1.19464i | ||||
\(233\) | −21.0000 | − | 21.0000i | −1.37576 | − | 1.37576i | −0.851658 | − | 0.524097i | \(-0.824403\pi\) |
−0.524097 | − | 0.851658i | \(-0.675597\pi\) | |||||||
\(234\) | −10.0981 | + | 11.4904i | −0.660132 | + | 0.751150i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.9904 | − | 25.9641i | −0.965615 | − | 1.67249i | −0.707953 | − | 0.706260i | \(-0.750381\pi\) |
−0.257663 | − | 0.966235i | \(-0.582952\pi\) | |||||||
\(242\) | −11.0000 | + | 11.0000i | −0.707107 | + | 0.707107i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −25.3923 | − | 14.6603i | −1.62558 | − | 0.938527i | ||||
\(245\) | 15.6244 | − | 0.937822i | 0.998203 | − | 0.0599153i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −14.2942 | + | 6.75833i | −0.904046 | + | 0.427434i | ||||
\(251\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.00000 | − | 13.8564i | −0.500000 | − | 0.866025i | ||||
\(257\) | 7.86603 | + | 29.3564i | 0.490669 | + | 1.83120i | 0.553047 | + | 0.833150i | \(0.313465\pi\) |
−0.0623783 | + | 0.998053i | \(0.519869\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 14.8564 | + | 6.26795i | 0.921355 | + | 0.388722i | ||||
\(261\) | 19.9808 | 1.23678 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.526279 | − | 0.107695i | −0.0323291 | − | 0.00661566i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 22.5167 | − | 13.0000i | 1.37287 | − | 0.792624i | 0.381577 | − | 0.924337i | \(-0.375381\pi\) |
0.991288 | + | 0.131713i | \(0.0420477\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(272\) | −11.3205 | + | 11.3205i | −0.686407 | + | 0.686407i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 32.9808i | 1.99244i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 21.6244 | + | 5.79423i | 1.29928 | + | 0.348141i | 0.841178 | − | 0.540758i | \(-0.181862\pi\) |
0.458103 | + | 0.888899i | \(0.348529\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7.33975 | −0.437853 | −0.218926 | − | 0.975741i | \(-0.570255\pi\) | ||||
−0.218926 | + | 0.975741i | \(0.570255\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −16.3923 | + | 4.39230i | −0.965926 | + | 0.258819i | ||||
\(289\) | −0.849365 | − | 0.490381i | −0.0499626 | − | 0.0288459i | ||||
\(290\) | −6.66025 | − | 19.9808i | −0.391104 | − | 1.17331i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −26.8564 | − | 7.19615i | −1.57165 | − | 0.421123i | ||||
\(293\) | 1.27757 | − | 4.76795i | 0.0746363 | − | 0.278547i | −0.918514 | − | 0.395388i | \(-0.870610\pi\) |
0.993151 | + | 0.116841i | \(0.0372769\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 1.66025 | − | 2.87564i | 0.0965003 | − | 0.167143i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −24.3205 | − | 24.3205i | −1.40885 | − | 1.40885i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 29.3205 | + | 14.6603i | 1.67889 | + | 0.839444i | ||||
\(306\) | 8.49038 | + | 14.7058i | 0.485363 | + | 0.840673i | ||||
\(307\) | 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 | ||||||||
\(313\) | −1.00000 | − | 1.00000i | −0.0565233 | − | 0.0565233i | 0.678280 | − | 0.734803i | \(-0.262726\pi\) |
−0.734803 | + | 0.678280i | \(0.762726\pi\) | |||||||
\(314\) | −22.2224 | − | 12.8301i | −1.25408 | − | 0.724046i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −23.1506 | + | 23.1506i | −1.30027 | + | 1.30027i | −0.372061 | + | 0.928208i | \(0.621349\pi\) |
−0.928208 | + | 0.372061i | \(0.878651\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 9.85641 | + | 14.9282i | 0.550990 | + | 0.834512i | ||||
\(321\) | 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 | ||||||||
\(328\) | −34.5885 | + | 9.26795i | −1.90983 | + | 0.511737i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.49038 | − | 2.49038i | −0.136472 | − | 0.136472i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 25.1506 | − | 25.1506i | 1.37004 | − | 1.37004i | 0.509676 | − | 0.860366i | \(-0.329765\pi\) |
0.860366 | − | 0.509676i | \(-0.170235\pi\) | |||||||
\(338\) | 7.00000 | + | 17.0000i | 0.380750 | + | 0.924678i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 11.8756 | − | 13.3923i | 0.644047 | − | 0.726300i | ||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 22.0000 | 1.18273 | ||||||||
\(347\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −31.1769 | − | 18.0000i | −1.66886 | − | 0.963518i | −0.968253 | − | 0.249973i | \(-0.919578\pi\) |
−0.700609 | − | 0.713545i | \(-0.747088\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −23.4282 | + | 6.27757i | −1.24696 | + | 0.334121i | −0.821160 | − | 0.570697i | \(-0.806673\pi\) |
−0.425797 | + | 0.904819i | \(0.640006\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 32.0000 | 1.69600 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(360\) | 18.0000 | − | 6.00000i | 0.948683 | − | 0.316228i | ||||
\(361\) | 9.50000 | − | 16.4545i | 0.500000 | − | 0.866025i | ||||
\(362\) | −9.63397 | − | 35.9545i | −0.506350 | − | 1.88973i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 30.4545 | + | 6.23205i | 1.59406 | + | 0.326200i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 37.9808i | 1.97720i | ||||||||
\(370\) | −1.66025 | + | 3.32051i | −0.0863125 | + | 0.172625i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.93782 | − | 37.0885i | 0.514561 | − | 1.92037i | 0.152115 | − | 0.988363i | \(-0.451392\pi\) |
0.362446 | − | 0.932005i | \(-0.381942\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 10.6436 | − | 21.5263i | 0.548173 | − | 1.10866i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −13.8301 | − | 23.9545i | −0.703935 | − | 1.21925i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 35.5167 | − | 9.51666i | 1.80309 | − | 0.483135i | ||||
\(389\) | − | 0.320508i | − | 0.0162504i | −0.999967 | − | 0.00812520i | \(-0.997414\pi\) | ||
0.999967 | − | 0.00812520i | \(-0.00258636\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 5.12436 | + | 19.1244i | 0.258819 | + | 0.965926i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 22.5167 | − | 13.0000i | 1.13437 | − | 0.654931i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −17.7583 | − | 4.75833i | −0.891265 | − | 0.238814i | −0.216004 | − | 0.976392i | \(-0.569302\pi\) |
−0.675261 | + | 0.737579i | \(0.735969\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −12.0000 | − | 16.0000i | −0.600000 | − | 0.800000i | ||||
\(401\) | 17.8205 | − | 30.8660i | 0.889914 | − | 1.54138i | 0.0499376 | − | 0.998752i | \(-0.484098\pi\) |
0.839976 | − | 0.542623i | \(-0.182569\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | − | 32.6410i | − | 1.62395i | ||||||
\(405\) | −1.20577 | − | 20.0885i | −0.0599153 | − | 0.998203i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −32.5981 | + | 18.8205i | −1.61187 | + | 0.930614i | −0.622935 | + | 0.782274i | \(0.714060\pi\) |
−0.988936 | + | 0.148340i | \(0.952607\pi\) | |||||||
\(410\) | 37.9808 | − | 12.6603i | 1.87574 | − | 0.625245i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −4.00000 | + | 20.0000i | −0.196116 | + | 0.980581i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11.9808 | −0.583907 | −0.291953 | − | 0.956433i | \(-0.594305\pi\) | ||||
−0.291953 | + | 0.956433i | \(0.594305\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | − | 0.679492i | − | 0.0329990i | ||||||
\(425\) | −12.3564 | + | 15.7417i | −0.599374 | + | 0.763583i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.72243 | + | 13.8923i | −0.178889 | + | 0.667622i | 0.816968 | + | 0.576683i | \(0.195653\pi\) |
−0.995857 | + | 0.0909384i | \(0.971013\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −6.00000 | − | 10.3923i | −0.287348 | − | 0.497701i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 21.0000 | 1.00000 | ||||||||
\(442\) | 20.3660 | − | 1.31347i | 0.968713 | − | 0.0624752i | ||||
\(443\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −35.7128 | + | 2.14359i | −1.69295 | + | 0.101616i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −12.1244 | + | 7.00000i | −0.572184 | + | 0.330350i | −0.758021 | − | 0.652230i | \(-0.773834\pi\) |
0.185837 | + | 0.982581i | \(0.440500\pi\) | |||||||
\(450\) | −19.6865 | + | 7.90192i | −0.928032 | + | 0.372500i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −9.14359 | − | 34.1244i | −0.430078 | − | 1.60507i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11.0359 | + | 41.1865i | 0.516238 | + | 1.92662i | 0.329125 | + | 0.944286i | \(0.393246\pi\) |
0.187112 | + | 0.982339i | \(0.440087\pi\) | |||||||
\(458\) | −5.46410 | + | 1.46410i | −0.255321 | + | 0.0684130i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −0.839746 | − | 1.45448i | −0.0391109 | − | 0.0677420i | 0.845807 | − | 0.533488i | \(-0.179119\pi\) |
−0.884918 | + | 0.465746i | \(0.845786\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(464\) | 23.0718 | − | 13.3205i | 1.07108 | − | 0.618389i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −21.0000 | + | 36.3731i | −0.972806 | + | 1.68495i | ||||
\(467\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(468\) | 19.3923 | + | 9.58846i | 0.896410 | + | 0.443227i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.696152 | − | 0.186533i | −0.0318746 | − | 0.00854078i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.00962 | + | 1.35641i | −0.182823 | + | 0.0618468i | ||||
\(482\) | −29.9808 | + | 29.9808i | −1.36559 | + | 1.36559i | ||||
\(483\) | 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 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(488\) | −10.7321 | + | 40.0526i | −0.485817 | + | 1.81309i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −7.00000 | − | 21.0000i | −0.316228 | − | 0.948683i | ||||
\(491\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −18.8494 | − | 18.8494i | −0.848933 | − | 0.848933i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(500\) | 14.4641 | + | 17.0526i | 0.646854 | + | 0.762614i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.18653 | + | 36.4282i | 0.0972995 | + | 1.62103i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −11.5526 | − | 6.66987i | −0.512058 | − | 0.295637i | 0.221621 | − | 0.975133i | \(-0.428865\pi\) |
−0.733679 | + | 0.679496i | \(0.762199\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −16.0000 | + | 16.0000i | −0.707107 | + | 0.707107i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 37.2224 | − | 21.4904i | 1.64181 | − | 0.947900i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 3.12436 | − | 22.5885i | 0.137012 | − | 0.990569i | ||||
\(521\) | −45.6410 | −1.99957 | −0.999785 | − | 0.0207541i | \(-0.993393\pi\) | ||||
−0.999785 | + | 0.0207541i | \(0.993393\pi\) | |||||||
\(522\) | −7.31347 | − | 27.2942i | −0.320102 | − | 1.19464i | ||||
\(523\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 19.9186 | − | 11.5000i | 0.866025 | − | 0.500000i | ||||
\(530\) | 0.0455173 | + | 0.758330i | 0.00197715 | + | 0.0329398i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 40.9186 | + | 20.2321i | 1.77238 | + | 0.876347i | ||||
\(534\) | 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 | ||||||||
\(541\) | −38.3205 | −1.64753 | −0.823764 | − | 0.566933i | \(-0.808130\pi\) | ||||
−0.823764 | + | 0.566933i | \(0.808130\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 19.6077 | + | 11.3205i | 0.840673 | + | 0.485363i | ||||
\(545\) | 7.39230 | + | 11.1962i | 0.316652 | + | 0.479590i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(548\) | 45.0526 | − | 12.0718i | 1.92455 | − | 0.515682i | ||||
\(549\) | 38.0885 | + | 21.9904i | 1.62558 | + | 0.938527i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | − | 31.6603i | − | 1.34512i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −4.45448 | − | 16.6244i | −0.188742 | − | 0.704397i | −0.993798 | − | 0.111198i | \(-0.964531\pi\) |
0.805056 | − | 0.593199i | \(-0.202135\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 2.68653 | + | 10.0263i | 0.113325 | + | 0.422933i | ||||
\(563\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 12.4904 | + | 37.4711i | 0.525474 | + | 1.57642i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −22.5167 | − | 13.0000i | −0.943948 | − | 0.544988i | −0.0527519 | − | 0.998608i | \(-0.516799\pi\) |
−0.891196 | + | 0.453619i | \(0.850133\pi\) | |||||||
\(570\) | 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 | ||||
\(577\) | 10.1506 | − | 10.1506i | 0.422576 | − | 0.422576i | −0.463513 | − | 0.886090i | \(-0.653411\pi\) |
0.886090 | + | 0.463513i | \(0.153411\pi\) | |||||||
\(578\) | −0.358984 | + | 1.33975i | −0.0149318 | + | 0.0557261i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −24.8564 | + | 16.4115i | −1.03211 | + | 0.681452i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 39.3205i | 1.62709i | ||||||||
\(585\) | −22.2846 | − | 9.40192i | −0.921355 | − | 0.388722i | ||||
\(586\) | −6.98076 | −0.288373 | ||||||||
\(587\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −4.53590 | − | 1.21539i | −0.186424 | − | 0.0499522i | ||||
\(593\) | 28.4904 | + | 28.4904i | 1.16996 | + | 1.16996i | 0.982219 | + | 0.187741i | \(0.0601166\pi\) |
0.187741 | + | 0.982219i | \(0.439883\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −24.3205 | + | 42.1244i | −0.996207 | + | 1.72548i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −16.3301 | + | 28.2846i | −0.666120 | + | 1.15375i | 0.312861 | + | 0.949799i | \(0.398713\pi\) |
−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 | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 9.29423 | − | 45.4186i | 0.376312 | − | 1.83894i | ||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 16.9808 | − | 16.9808i | 0.686407 | − | 0.686407i | ||||
\(613\) | 40.7224 | − | 10.9115i | 1.64476 | − | 0.440713i | 0.686624 | − | 0.727013i | \(-0.259092\pi\) |
0.958140 | + | 0.286300i | \(0.0924254\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 43.4545 | + | 11.6436i | 1.74941 | + | 0.468753i | 0.984500 | − | 0.175382i | \(-0.0561162\pi\) |
0.764911 | + | 0.644136i | \(0.222783\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −17.2846 | − | 18.0622i | −0.691384 | − | 0.722487i | ||||
\(626\) | −1.00000 | + | 1.73205i | −0.0399680 | + | 0.0692267i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −9.39230 | + | 35.0526i | −0.374794 | + | 1.39875i | ||||
\(629\) | 4.69873i | 0.187351i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 40.0981 | + | 23.1506i | 1.59250 | + | 0.919429i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 11.1865 | − | 22.6244i | 0.443227 | − | 0.896410i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 16.7846 | − | 18.9282i | 0.663470 | − | 0.748203i | ||||
\(641\) | −23.6506 | − | 40.9641i | −0.934144 | − | 1.61798i | −0.776153 | − | 0.630544i | \(-0.782832\pi\) |
−0.157991 | − | 0.987441i | \(-0.550502\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(648\) | 24.5885 | − | 6.58846i | 0.965926 | − | 0.258819i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −1.97372 | + | 25.4186i | −0.0774157 | + | 0.996999i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −12.2942 | + | 3.29423i | −0.481110 | + | 0.128913i | −0.491220 | − | 0.871036i | \(-0.663449\pi\) |
0.0101092 | + | 0.999949i | \(0.496782\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 25.3205 | + | 43.8564i | 0.988600 | + | 1.71230i | ||||
\(657\) | 40.2846 | + | 10.7942i | 1.57165 | + | 0.421123i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −18.6506 | + | 32.3038i | −0.725426 | + | 1.25647i | 0.233373 | + | 0.972387i | \(0.425024\pi\) |
−0.958799 | + | 0.284087i | \(0.908310\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −2.49038 | + | 4.31347i | −0.0965003 | + | 0.167143i | ||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 33.8923 | − | 9.08142i | 1.30645 | − | 0.350063i | 0.462566 | − | 0.886585i | \(-0.346929\pi\) |
0.843886 | + | 0.536522i | \(0.180262\pi\) | |||||||
\(674\) | −43.5622 | − | 25.1506i | −1.67795 | − | 0.968766i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 20.6603 | − | 15.7846i | 0.794625 | − | 0.607100i | ||||
\(677\) | −27.0000 | + | 27.0000i | −1.03769 | + | 1.03769i | −0.0384331 | + | 0.999261i | \(0.512237\pi\) |
−0.999261 | + | 0.0384331i | \(0.987763\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −22.6410 | − | 11.3205i | −0.868243 | − | 0.434122i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −49.4711 | + | 16.4904i | −1.89020 | + | 0.630065i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.571797 | + | 0.650635i | −0.0217837 | + | 0.0247872i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(692\) | −8.05256 | − | 30.0526i | −0.306112 | − | 1.14243i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 35.8301 | − | 35.8301i | 1.35716 | − | 1.35716i | ||||
\(698\) | −13.1769 | + | 49.1769i | −0.498754 | + | 1.86137i | ||||
\(699\) | 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 | ||||||||
\(706\) | 17.1506 | + | 29.7058i | 0.645473 | + | 1.11799i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.44744 | + | 1.99038i | −0.129471 | + | 0.0747503i | −0.563337 | − | 0.826227i | \(-0.690483\pi\) |
0.433865 | + | 0.900978i | \(0.357149\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −11.7128 | − | 43.7128i | −0.438956 | − | 1.63821i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(720\) | −14.7846 | − | 22.3923i | −0.550990 | − | 0.834512i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −25.9545 | − | 6.95448i | −0.965926 | − | 0.258819i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −45.5885 | + | 26.3205i | −1.69428 | + | 0.978194i | ||||
\(725\) | 26.6410 | − | 19.9808i | 0.989423 | − | 0.742067i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 27.0000i | − | 1.00000i | ||||||
\(730\) | −2.63397 | − | 43.8827i | −0.0974878 | − | 1.62417i | ||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −36.1506 | − | 36.1506i | −1.33525 | − | 1.33525i | −0.900595 | − | 0.434659i | \(-0.856869\pi\) |
−0.434659 | − | 0.900595i | \(-0.643131\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 51.8827 | − | 13.9019i | 1.90983 | − | 0.511737i | ||||
\(739\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(740\) | 5.14359 | + | 1.05256i | 0.189082 | + | 0.0386928i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 24.3205 | − | 48.6410i | 0.891034 | − | 1.78207i | ||||
\(746\) | −54.3013 | −1.98811 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −33.3013 | − | 6.66025i | −1.21276 | − | 0.242552i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −6.22243 | − | 23.2224i | −0.226158 | − | 0.844034i | −0.981937 | − | 0.189207i | \(-0.939408\pi\) |
0.755779 | − | 0.654827i | \(-0.227258\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 19.0000 | + | 32.9090i | 0.688749 | + | 1.19295i | 0.972243 | + | 0.233975i | \(0.0751733\pi\) |
−0.283493 | + | 0.958974i | \(0.591493\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −17.8135 | + | 20.0885i | −0.644047 | + | 0.726300i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 20.7846 | + | 12.0000i | 0.749512 | + | 0.432731i | 0.825518 | − | 0.564376i | \(-0.190883\pi\) |
−0.0760054 | + | 0.997107i | \(0.524217\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −27.6603 | + | 27.6603i | −0.995514 | + | 0.995514i | ||||
\(773\) | 14.2750 | − | 53.2750i | 0.513436 | − | 1.91617i | 0.133887 | − | 0.990997i | \(-0.457254\pi\) |
0.379549 | − | 0.925172i | \(-0.376079\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −26.0000 | − | 45.0333i | −0.933346 | − | 1.61660i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −0.437822 | + | 0.117314i | −0.0156967 | + | 0.00420591i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 24.2487 | − | 14.0000i | 0.866025 | − | 0.500000i | ||||
\(785\) | 8.13397 | − | 39.7487i | 0.290314 | − | 1.41869i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(788\) | −26.0000 | − | 26.0000i | −0.926212 | − | 0.926212i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 43.9808 | − | 29.3205i | 1.56180 | − | 1.04120i | ||||
\(794\) | 26.0000i | 0.922705i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 50.5429 | + | 13.5429i | 1.79032 | + | 0.479716i | 0.992401 | − | 0.123045i | \(-0.0392661\pi\) |
0.797922 | + | 0.602761i | \(0.205933\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −17.4641 | + | 22.2487i | −0.617449 | + | 0.786611i | ||||
\(801\) | −48.0000 | −1.69600 | ||||||||
\(802\) | −48.6865 | − | 13.0455i | −1.71918 | − | 0.460653i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −44.5885 | + | 11.9474i | −1.56862 | + | 0.420310i | ||||
\(809\) | 16.7487 | + | 9.66987i | 0.588853 | + | 0.339975i | 0.764644 | − | 0.644453i | \(-0.222915\pi\) |
−0.175791 | + | 0.984428i | \(0.556248\pi\) | |||||||
\(810\) | −27.0000 | + | 9.00000i | −0.948683 | + | 0.316228i | ||||
\(811\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 37.6410 | + | 37.6410i | 1.31609 | + | 1.31609i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −31.1962 | − | 47.2487i | −1.08942 | − | 1.65000i | ||||
\(821\) | 14.0000 | − | 24.2487i | 0.488603 | − | 0.846286i | −0.511311 | − | 0.859396i | \(-0.670840\pi\) |
0.999914 | + | 0.0131101i | \(0.00417319\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(824\) | 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 | ||||||||
\(829\) | −8.38269 | − | 4.83975i | −0.291143 | − | 0.168091i | 0.347314 | − | 0.937749i | \(-0.387094\pi\) |
−0.638457 | + | 0.769657i | \(0.720427\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 28.7846 | − | 1.85641i | 0.997927 | − | 0.0643593i | ||||
\(833\) | −19.8109 | − | 19.8109i | −0.686407 | − | 0.686407i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.67949 | + | 13.3013i | 0.264810 | + | 0.458664i | ||||
\(842\) | 4.38526 | + | 16.3660i | 0.151126 | + | 0.564010i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −22.0000 | + | 19.0000i | −0.756823 | + | 0.653620i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −0.928203 | + | 0.248711i | −0.0318746 | + | 0.00854078i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 26.0263 | + | 11.1173i | 0.892694 | + | 0.381321i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 16.1699 | + | 16.1699i | 0.553646 | + | 0.553646i | 0.927491 | − | 0.373845i | \(-0.121961\pi\) |
−0.373845 | + | 0.927491i | \(0.621961\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −38.1506 | + | 38.1506i | −1.30320 | + | 1.30320i | −0.376979 | + | 0.926222i | \(0.623037\pi\) |
−0.926222 | + | 0.376979i | \(0.876963\pi\) | |||||||
\(858\) | 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 | ||||||||
\(865\) | 11.0000 | + | 33.0000i | 0.374011 | + | 1.12203i | ||||
\(866\) | 20.3397 | 0.691173 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −12.0000 | + | 12.0000i | −0.406371 | + | 0.406371i | ||||
\(873\) | −53.2750 | + | 14.2750i | −1.80309 | + | 0.483135i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −25.6962 | − | 6.88526i | −0.867697 | − | 0.232499i | −0.202606 | − | 0.979260i | \(-0.564941\pi\) |
−0.665092 | + | 0.746762i | \(0.731608\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 29.6506 | − | 51.3564i | 0.998955 | − | 1.73024i | 0.459902 | − | 0.887970i | \(-0.347885\pi\) |
0.539054 | − | 0.842271i | \(-0.318782\pi\) | |||||||
\(882\) | −7.68653 | − | 28.6865i | −0.258819 | − | 0.965926i | ||||
\(883\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(884\) | −9.24871 | − | 27.3397i | −0.311068 | − | 0.919535i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 16.0000 | + | 48.0000i | 0.536321 | + | 1.60896i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 14.0000 | + | 14.0000i | 0.467186 | + | 0.467186i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 18.0000 | + | 24.0000i | 0.600000 | + | 0.800000i | ||||
\(901\) | 0.480762 | + | 0.832704i | 0.0160165 | + | 0.0277414i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −43.2679 | + | 24.9808i | −1.43907 | + | 0.830848i | ||||
\(905\) | 49.1147 | − | 32.4282i | 1.63263 | − | 1.07795i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 48.9615i | 1.62395i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 52.2224 | − | 30.1506i | 1.72736 | − | 0.997294i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 4.00000 | + | 6.92820i | 0.132164 | + | 0.228914i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −1.67949 | + | 1.67949i | −0.0553111 | + | 0.0553111i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.81089 | − | 0.830127i | −0.191061 | − | 0.0272944i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −26.6410 | − | 26.6410i | −0.874534 | − | 0.874534i | ||||
\(929\) | 10.0814 | − | 5.82051i | 0.330761 | − | 0.190965i | −0.325418 | − | 0.945570i | \(-0.605505\pi\) |
0.656179 | + | 0.754606i | \(0.272172\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 57.3731 | + | 15.3731i | 1.87932 | + | 0.503562i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 6.00000 | − | 30.0000i | 0.196116 | − | 0.980581i | ||||
\(937\) | −25.8301 | + | 25.8301i | −0.843833 | + | 0.843833i | −0.989355 | − | 0.145522i | \(-0.953514\pi\) |
0.145522 | + | 0.989355i | \(0.453514\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −58.0000 | −1.89075 | −0.945373 | − | 0.325991i | \(-0.894302\pi\) | ||||
−0.945373 | + | 0.325991i | \(0.894302\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 33.0885 | − | 37.6506i | 1.07410 | − | 1.22219i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −15.0070 | + | 56.0070i | −0.486126 | + | 1.81425i | 0.0888114 | + | 0.996048i | \(0.471693\pi\) |
−0.574937 | + | 0.818198i | \(0.694974\pi\) | |||||||
\(954\) | 1.01924i | 0.0329990i | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 31.0000 | 1.00000 | ||||||||
\(962\) | 3.32051 | + | 4.98076i | 0.107057 | + | 0.160586i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 51.9282 | + | 29.9808i | 1.67249 | + | 0.965615i | ||||
\(965\) | 29.0167 | − | 32.7224i | 0.934079 | − | 1.05337i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(968\) | 8.05256 | − | 30.0526i | 0.258819 | − | 0.965926i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 32.0333 | + | 48.5167i | 1.02853 | + | 1.55778i | ||||
\(971\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 58.6410 | 1.87705 | ||||||||
\(977\) | −6.15321 | − | 22.9641i | −0.196859 | − | 0.734687i | −0.991778 | − | 0.127971i | \(-0.959153\pi\) |
0.794919 | − | 0.606715i | \(-0.207513\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −26.1244 | + | 17.2487i | −0.834512 | + | 0.550990i | ||||
\(981\) | 9.00000 | + | 15.5885i | 0.287348 | + | 0.497701i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 30.7583 | + | 27.2750i | 0.980042 | + | 0.869053i | ||||
\(986\) | −18.8494 | + | 32.6481i | −0.600286 | + | 1.03973i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −54.8468 | − | 14.6962i | −1.73702 | − | 0.465432i | −0.755235 | − | 0.655454i | \(-0.772477\pi\) |
−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.bj.a.243.1 | yes | 4 | |
4.3 | odd | 2 | CM | 260.2.bj.a.243.1 | yes | 4 | |
5.2 | odd | 4 | 260.2.bj.b.87.1 | yes | 4 | ||
13.3 | even | 3 | 260.2.bj.b.3.1 | yes | 4 | ||
20.7 | even | 4 | 260.2.bj.b.87.1 | yes | 4 | ||
52.3 | odd | 6 | 260.2.bj.b.3.1 | yes | 4 | ||
65.42 | odd | 12 | inner | 260.2.bj.a.107.1 | ✓ | 4 | |
260.107 | even | 12 | inner | 260.2.bj.a.107.1 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
260.2.bj.a.107.1 | ✓ | 4 | 65.42 | odd | 12 | inner | |
260.2.bj.a.107.1 | ✓ | 4 | 260.107 | even | 12 | inner | |
260.2.bj.a.243.1 | yes | 4 | 1.1 | even | 1 | trivial | |
260.2.bj.a.243.1 | yes | 4 | 4.3 | odd | 2 | CM | |
260.2.bj.b.3.1 | yes | 4 | 13.3 | even | 3 | ||
260.2.bj.b.3.1 | yes | 4 | 52.3 | odd | 6 | ||
260.2.bj.b.87.1 | yes | 4 | 5.2 | odd | 4 | ||
260.2.bj.b.87.1 | yes | 4 | 20.7 | even | 4 |