Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1710,2,Mod(1369,1710)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1710, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1710.1369");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1710.d (of order \(2\), degree \(1\), 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: | \(13.6544187456\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.350464.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 570) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1369.1 | ||
Root | \(1.45161 + 1.45161i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1710.1369 |
Dual form | 1710.2.d.f.1369.4 |
$q$-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 \(\left(\mathbb{Z}/1710\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(1027\) | \(1351\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.00000i | − | 0.707107i | ||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | −2.21432 | + | 0.311108i | −0.990274 | + | 0.139132i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 4.42864i | − | 1.67387i | −0.547304 | − | 0.836934i | \(-0.684346\pi\) | ||
0.547304 | − | 0.836934i | \(-0.315654\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.311108 | + | 2.21432i | 0.0983809 | + | 0.700229i | ||||
\(11\) | −2.62222 | −0.790628 | −0.395314 | − | 0.918546i | \(-0.629364\pi\) | ||||
−0.395314 | + | 0.918546i | \(0.629364\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 5.80642i | − | 1.61041i | −0.592995 | − | 0.805206i | \(-0.702055\pi\) | ||
0.592995 | − | 0.805206i | \(-0.297945\pi\) | |||||||
\(14\) | −4.42864 | −1.18360 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 3.80642i | 0.923193i | 0.887090 | + | 0.461597i | \(0.152723\pi\) | ||||
−0.887090 | + | 0.461597i | \(0.847277\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 2.21432 | − | 0.311108i | 0.495137 | − | 0.0695658i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.62222i | 0.559058i | ||||||||
\(23\) | − | 2.62222i | − | 0.546770i | −0.961905 | − | 0.273385i | \(-0.911857\pi\) | ||
0.961905 | − | 0.273385i | \(-0.0881433\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.80642 | − | 1.37778i | 0.961285 | − | 0.275557i | ||||
\(26\) | −5.80642 | −1.13873 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 4.42864i | 0.836934i | ||||||||
\(29\) | 3.37778 | 0.627239 | 0.313619 | − | 0.949549i | \(-0.398458\pi\) | ||||
0.313619 | + | 0.949549i | \(0.398458\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.42864 | −0.795407 | −0.397704 | − | 0.917514i | \(-0.630193\pi\) | ||||
−0.397704 | + | 0.917514i | \(0.630193\pi\) | |||||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.80642 | 0.652796 | ||||||||
\(35\) | 1.37778 | + | 9.80642i | 0.232888 | + | 1.65759i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.80642i | 0.954570i | 0.878749 | + | 0.477285i | \(0.158379\pi\) | ||||
−0.878749 | + | 0.477285i | \(0.841621\pi\) | |||||||
\(38\) | 1.00000i | 0.162221i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.311108 | − | 2.21432i | −0.0491905 | − | 0.350115i | ||||
\(41\) | −5.67307 | −0.885985 | −0.442992 | − | 0.896525i | \(-0.646083\pi\) | ||||
−0.442992 | + | 0.896525i | \(0.646083\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.9906i | 1.67606i | 0.545627 | + | 0.838028i | \(0.316291\pi\) | ||||
−0.545627 | + | 0.838028i | \(0.683709\pi\) | |||||||
\(44\) | 2.62222 | 0.395314 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.62222 | −0.386625 | ||||||||
\(47\) | − | 2.62222i | − | 0.382489i | −0.981542 | − | 0.191245i | \(-0.938748\pi\) | ||
0.981542 | − | 0.191245i | \(-0.0612524\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −12.6128 | −1.80184 | ||||||||
\(50\) | −1.37778 | − | 4.80642i | −0.194848 | − | 0.679731i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 5.80642i | 0.805206i | ||||||||
\(53\) | − | 6.00000i | − | 0.824163i | −0.911147 | − | 0.412082i | \(-0.864802\pi\) | ||
0.911147 | − | 0.412082i | \(-0.135198\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.80642 | − | 0.815792i | 0.782938 | − | 0.110001i | ||||
\(56\) | 4.42864 | 0.591802 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | − | 3.37778i | − | 0.443525i | ||||||
\(59\) | −1.05086 | −0.136810 | −0.0684048 | − | 0.997658i | \(-0.521791\pi\) | ||||
−0.0684048 | + | 0.997658i | \(0.521791\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.75557 | 0.608888 | 0.304444 | − | 0.952530i | \(-0.401529\pi\) | ||||
0.304444 | + | 0.952530i | \(0.401529\pi\) | |||||||
\(62\) | 4.42864i | 0.562438i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 1.80642 | + | 12.8573i | 0.224059 | + | 1.59475i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 15.6128i | 1.90741i | 0.300739 | + | 0.953706i | \(0.402767\pi\) | ||||
−0.300739 | + | 0.953706i | \(0.597233\pi\) | |||||||
\(68\) | − | 3.80642i | − | 0.461597i | ||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 9.80642 | − | 1.37778i | 1.17209 | − | 0.164677i | ||||
\(71\) | −15.6128 | −1.85290 | −0.926452 | − | 0.376413i | \(-0.877157\pi\) | ||||
−0.926452 | + | 0.376413i | \(0.877157\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 11.6128i | − | 1.35918i | −0.733592 | − | 0.679591i | \(-0.762157\pi\) | ||
0.733592 | − | 0.679591i | \(-0.237843\pi\) | |||||||
\(74\) | 5.80642 | 0.674983 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.00000 | 0.114708 | ||||||||
\(77\) | 11.6128i | 1.32341i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.42864 | −0.498261 | −0.249130 | − | 0.968470i | \(-0.580145\pi\) | ||||
−0.249130 | + | 0.968470i | \(0.580145\pi\) | |||||||
\(80\) | −2.21432 | + | 0.311108i | −0.247568 | + | 0.0347829i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 5.67307i | 0.626486i | ||||||||
\(83\) | 11.9081i | 1.30709i | 0.756889 | + | 0.653544i | \(0.226718\pi\) | ||||
−0.756889 | + | 0.653544i | \(0.773282\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.18421 | − | 8.42864i | −0.128445 | − | 0.914214i | ||||
\(86\) | 10.9906 | 1.18515 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − | 2.62222i | − | 0.279529i | ||||||
\(89\) | 12.4286 | 1.31743 | 0.658717 | − | 0.752391i | \(-0.271100\pi\) | ||||
0.658717 | + | 0.752391i | \(0.271100\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −25.7146 | −2.69562 | ||||||||
\(92\) | 2.62222i | 0.273385i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −2.62222 | −0.270461 | ||||||||
\(95\) | 2.21432 | − | 0.311108i | 0.227184 | − | 0.0319190i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.37778i | 0.749101i | 0.927207 | + | 0.374550i | \(0.122203\pi\) | ||||
−0.927207 | + | 0.374550i | \(0.877797\pi\) | |||||||
\(98\) | 12.6128i | 1.27409i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −4.80642 | + | 1.37778i | −0.480642 | + | 0.137778i | ||||
\(101\) | −17.6731 | −1.75854 | −0.879268 | − | 0.476327i | \(-0.841968\pi\) | ||||
−0.879268 | + | 0.476327i | \(0.841968\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.18421i | 0.116684i | 0.998297 | + | 0.0583418i | \(0.0185813\pi\) | ||||
−0.998297 | + | 0.0583418i | \(0.981419\pi\) | |||||||
\(104\) | 5.80642 | 0.569367 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.00000 | −0.582772 | ||||||||
\(107\) | − | 4.85728i | − | 0.469571i | −0.972047 | − | 0.234785i | \(-0.924561\pi\) | ||
0.972047 | − | 0.234785i | \(-0.0754388\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.04149 | 0.578670 | 0.289335 | − | 0.957228i | \(-0.406566\pi\) | ||||
0.289335 | + | 0.957228i | \(0.406566\pi\) | |||||||
\(110\) | −0.815792 | − | 5.80642i | −0.0777827 | − | 0.553621i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − | 4.42864i | − | 0.418467i | ||||||
\(113\) | 9.34614i | 0.879211i | 0.898191 | + | 0.439606i | \(0.144882\pi\) | ||||
−0.898191 | + | 0.439606i | \(0.855118\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.815792 | + | 5.80642i | 0.0760730 | + | 0.541452i | ||||
\(116\) | −3.37778 | −0.313619 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.05086i | 0.0967391i | ||||||||
\(119\) | 16.8573 | 1.54530 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.12399 | −0.374908 | ||||||||
\(122\) | − | 4.75557i | − | 0.430549i | ||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 4.42864 | 0.397704 | ||||||||
\(125\) | −10.2143 | + | 4.54617i | −0.913597 | + | 0.406622i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.42864i | 0.570450i | 0.958461 | + | 0.285225i | \(0.0920682\pi\) | ||||
−0.958461 | + | 0.285225i | \(0.907932\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 12.8573 | − | 1.80642i | 1.12766 | − | 0.158434i | ||||
\(131\) | 15.0923 | 1.31862 | 0.659312 | − | 0.751869i | \(-0.270848\pi\) | ||||
0.659312 | + | 0.751869i | \(0.270848\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.42864i | 0.384012i | ||||||||
\(134\) | 15.6128 | 1.34874 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.80642 | −0.326398 | ||||||||
\(137\) | 7.53972i | 0.644162i | 0.946712 | + | 0.322081i | \(0.104382\pi\) | ||||
−0.946712 | + | 0.322081i | \(0.895618\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.387152 | −0.0328378 | −0.0164189 | − | 0.999865i | \(-0.505227\pi\) | ||||
−0.0164189 | + | 0.999865i | \(0.505227\pi\) | |||||||
\(140\) | −1.37778 | − | 9.80642i | −0.116444 | − | 0.828794i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 15.6128i | 1.31020i | ||||||||
\(143\) | 15.2257i | 1.27324i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −7.47949 | + | 1.05086i | −0.621138 | + | 0.0872688i | ||||
\(146\) | −11.6128 | −0.961086 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 5.80642i | − | 0.477285i | ||||||
\(149\) | −14.5303 | −1.19037 | −0.595186 | − | 0.803588i | \(-0.702922\pi\) | ||||
−0.595186 | + | 0.803588i | \(0.702922\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.69535 | 0.382102 | 0.191051 | − | 0.981580i | \(-0.438810\pi\) | ||||
0.191051 | + | 0.981580i | \(0.438810\pi\) | |||||||
\(152\) | − | 1.00000i | − | 0.0811107i | ||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 11.6128 | 0.935790 | ||||||||
\(155\) | 9.80642 | − | 1.37778i | 0.787671 | − | 0.110666i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 21.5210i | − | 1.71756i | −0.512343 | − | 0.858781i | \(-0.671222\pi\) | ||
0.512343 | − | 0.858781i | \(-0.328778\pi\) | |||||||
\(158\) | 4.42864i | 0.352324i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0.311108 | + | 2.21432i | 0.0245952 | + | 0.175057i | ||||
\(161\) | −11.6128 | −0.915221 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.23506i | 0.645020i | 0.946566 | + | 0.322510i | \(0.104527\pi\) | ||||
−0.946566 | + | 0.322510i | \(0.895473\pi\) | |||||||
\(164\) | 5.67307 | 0.442992 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 11.9081 | 0.924250 | ||||||||
\(167\) | − | 8.47013i | − | 0.655438i | −0.944775 | − | 0.327719i | \(-0.893720\pi\) | ||
0.944775 | − | 0.327719i | \(-0.106280\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −20.7146 | −1.59343 | ||||||||
\(170\) | −8.42864 | + | 1.18421i | −0.646447 | + | 0.0908246i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − | 10.9906i | − | 0.838028i | ||||||
\(173\) | − | 22.4701i | − | 1.70837i | −0.519967 | − | 0.854186i | \(-0.674056\pi\) | ||
0.519967 | − | 0.854186i | \(-0.325944\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −6.10171 | − | 21.2859i | −0.461246 | − | 1.60906i | ||||
\(176\) | −2.62222 | −0.197657 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − | 12.4286i | − | 0.931566i | ||||||
\(179\) | −2.94914 | −0.220429 | −0.110215 | − | 0.993908i | \(-0.535154\pi\) | ||||
−0.110215 | + | 0.993908i | \(0.535154\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 22.8988 | 1.70205 | 0.851026 | − | 0.525124i | \(-0.175981\pi\) | ||||
0.851026 | + | 0.525124i | \(0.175981\pi\) | |||||||
\(182\) | 25.7146i | 1.90609i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2.62222 | 0.193312 | ||||||||
\(185\) | −1.80642 | − | 12.8573i | −0.132811 | − | 0.945286i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 9.98126i | − | 0.729902i | ||||||
\(188\) | 2.62222i | 0.191245i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.311108 | − | 2.21432i | −0.0225701 | − | 0.160644i | ||||
\(191\) | 9.05086 | 0.654897 | 0.327448 | − | 0.944869i | \(-0.393811\pi\) | ||||
0.327448 | + | 0.944869i | \(0.393811\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 18.7239i | − | 1.34778i | −0.738833 | − | 0.673889i | \(-0.764623\pi\) | ||
0.738833 | − | 0.673889i | \(-0.235377\pi\) | |||||||
\(194\) | 7.37778 | 0.529694 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 12.6128 | 0.900918 | ||||||||
\(197\) | − | 0.888922i | − | 0.0633331i | −0.999498 | − | 0.0316665i | \(-0.989919\pi\) | ||
0.999498 | − | 0.0316665i | \(-0.0100815\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −21.7146 | −1.53930 | −0.769652 | − | 0.638464i | \(-0.779570\pi\) | ||||
−0.769652 | + | 0.638464i | \(0.779570\pi\) | |||||||
\(200\) | 1.37778 | + | 4.80642i | 0.0974241 | + | 0.339865i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 17.6731i | 1.24347i | ||||||||
\(203\) | − | 14.9590i | − | 1.04992i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 12.5620 | − | 1.76494i | 0.877368 | − | 0.123269i | ||||
\(206\) | 1.18421 | 0.0825077 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − | 5.80642i | − | 0.402603i | ||||||
\(209\) | 2.62222 | 0.181382 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.61285 | −0.248719 | −0.124359 | − | 0.992237i | \(-0.539688\pi\) | ||||
−0.124359 | + | 0.992237i | \(0.539688\pi\) | |||||||
\(212\) | 6.00000i | 0.412082i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −4.85728 | −0.332037 | ||||||||
\(215\) | −3.41927 | − | 24.3368i | −0.233192 | − | 1.65975i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 19.6128i | 1.33141i | ||||||||
\(218\) | − | 6.04149i | − | 0.409181i | ||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −5.80642 | + | 0.815792i | −0.391469 | + | 0.0550007i | ||||
\(221\) | 22.1017 | 1.48672 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 21.3876i | 1.43222i | 0.697987 | + | 0.716111i | \(0.254079\pi\) | ||||
−0.697987 | + | 0.716111i | \(0.745921\pi\) | |||||||
\(224\) | −4.42864 | −0.295901 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 9.34614 | 0.621696 | ||||||||
\(227\) | − | 8.47013i | − | 0.562182i | −0.959681 | − | 0.281091i | \(-0.909304\pi\) | ||
0.959681 | − | 0.281091i | \(-0.0906963\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 16.9590 | 1.12068 | 0.560341 | − | 0.828262i | \(-0.310670\pi\) | ||||
0.560341 | + | 0.828262i | \(0.310670\pi\) | |||||||
\(230\) | 5.80642 | − | 0.815792i | 0.382864 | − | 0.0537917i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.37778i | 0.221762i | ||||||||
\(233\) | − | 17.9081i | − | 1.17320i | −0.809876 | − | 0.586600i | \(-0.800466\pi\) | ||
0.809876 | − | 0.586600i | \(-0.199534\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.815792 | + | 5.80642i | 0.0532164 | + | 0.378769i | ||||
\(236\) | 1.05086 | 0.0684048 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | − | 16.8573i | − | 1.09270i | ||||||
\(239\) | −28.2766 | −1.82906 | −0.914529 | − | 0.404520i | \(-0.867438\pi\) | ||||
−0.914529 | + | 0.404520i | \(0.867438\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.5111 | −0.741498 | −0.370749 | − | 0.928733i | \(-0.620899\pi\) | ||||
−0.370749 | + | 0.928733i | \(0.620899\pi\) | |||||||
\(242\) | 4.12399i | 0.265100i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −4.75557 | −0.304444 | ||||||||
\(245\) | 27.9289 | − | 3.92396i | 1.78431 | − | 0.250692i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.80642i | 0.369454i | ||||||||
\(248\) | − | 4.42864i | − | 0.281219i | ||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 4.54617 | + | 10.2143i | 0.287525 | + | 0.646010i | ||||
\(251\) | 7.74620 | 0.488936 | 0.244468 | − | 0.969657i | \(-0.421387\pi\) | ||||
0.244468 | + | 0.969657i | \(0.421387\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.87601i | 0.432291i | ||||||||
\(254\) | 6.42864 | 0.403369 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 13.8796i | 0.865783i | 0.901446 | + | 0.432891i | \(0.142507\pi\) | ||||
−0.901446 | + | 0.432891i | \(0.857493\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 25.7146 | 1.59782 | ||||||||
\(260\) | −1.80642 | − | 12.8573i | −0.112030 | − | 0.797375i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − | 15.0923i | − | 0.932408i | ||||||
\(263\) | − | 18.6222i | − | 1.14830i | −0.818752 | − | 0.574148i | \(-0.805334\pi\) | ||
0.818752 | − | 0.574148i | \(-0.194666\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.86665 | + | 13.2859i | 0.114667 | + | 0.816147i | ||||
\(266\) | 4.42864 | 0.271537 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − | 15.6128i | − | 0.953706i | ||||||
\(269\) | 15.8479 | 0.966264 | 0.483132 | − | 0.875547i | \(-0.339499\pi\) | ||||
0.483132 | + | 0.875547i | \(0.339499\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.51114 | 0.0917951 | 0.0458975 | − | 0.998946i | \(-0.485385\pi\) | ||||
0.0458975 | + | 0.998946i | \(0.485385\pi\) | |||||||
\(272\) | 3.80642i | 0.230798i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 7.53972 | 0.455491 | ||||||||
\(275\) | −12.6035 | + | 3.61285i | −0.760018 | + | 0.217863i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.05086i | 0.0631398i | 0.999502 | + | 0.0315699i | \(0.0100507\pi\) | ||||
−0.999502 | + | 0.0315699i | \(0.989949\pi\) | |||||||
\(278\) | 0.387152i | 0.0232199i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −9.80642 | + | 1.37778i | −0.586046 | + | 0.0823384i | ||||
\(281\) | −3.45091 | −0.205864 | −0.102932 | − | 0.994688i | \(-0.532822\pi\) | ||||
−0.102932 | + | 0.994688i | \(0.532822\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 15.5812i | − | 0.926206i | −0.886304 | − | 0.463103i | \(-0.846736\pi\) | ||
0.886304 | − | 0.463103i | \(-0.153264\pi\) | |||||||
\(284\) | 15.6128 | 0.926452 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 15.2257 | 0.900314 | ||||||||
\(287\) | 25.1240i | 1.48302i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.51114 | 0.147714 | ||||||||
\(290\) | 1.05086 | + | 7.47949i | 0.0617083 | + | 0.439211i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 11.6128i | 0.679591i | ||||||||
\(293\) | 7.12399i | 0.416188i | 0.978109 | + | 0.208094i | \(0.0667259\pi\) | ||||
−0.978109 | + | 0.208094i | \(0.933274\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.32693 | − | 0.326929i | 0.135479 | − | 0.0190346i | ||||
\(296\) | −5.80642 | −0.337492 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 14.5303i | 0.841721i | ||||||||
\(299\) | −15.2257 | −0.880525 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 48.6735 | 2.80550 | ||||||||
\(302\) | − | 4.69535i | − | 0.270187i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.00000 | −0.0573539 | ||||||||
\(305\) | −10.5303 | + | 1.47949i | −0.602966 | + | 0.0847156i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.12399i | 0.0641492i | 0.999485 | + | 0.0320746i | \(0.0102114\pi\) | ||||
−0.999485 | + | 0.0320746i | \(0.989789\pi\) | |||||||
\(308\) | − | 11.6128i | − | 0.661703i | ||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1.37778 | − | 9.80642i | −0.0782529 | − | 0.556967i | ||||
\(311\) | −14.9491 | −0.847688 | −0.423844 | − | 0.905735i | \(-0.639320\pi\) | ||||
−0.423844 | + | 0.905735i | \(0.639320\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 3.14272i | − | 0.177637i | −0.996048 | − | 0.0888185i | \(-0.971691\pi\) | ||
0.996048 | − | 0.0888185i | \(-0.0283091\pi\) | |||||||
\(314\) | −21.5210 | −1.21450 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4.42864 | 0.249130 | ||||||||
\(317\) | − | 10.5906i | − | 0.594826i | −0.954749 | − | 0.297413i | \(-0.903876\pi\) | ||
0.954749 | − | 0.297413i | \(-0.0961238\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.85728 | −0.495912 | ||||||||
\(320\) | 2.21432 | − | 0.311108i | 0.123784 | − | 0.0173915i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 11.6128i | 0.647159i | ||||||||
\(323\) | − | 3.80642i | − | 0.211795i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −8.00000 | − | 27.9081i | −0.443760 | − | 1.54806i | ||||
\(326\) | 8.23506 | 0.456098 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 5.67307i | − | 0.313243i | ||||||
\(329\) | −11.6128 | −0.640237 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −15.1427 | −0.832319 | −0.416160 | − | 0.909292i | \(-0.636624\pi\) | ||||
−0.416160 | + | 0.909292i | \(0.636624\pi\) | |||||||
\(332\) | − | 11.9081i | − | 0.653544i | ||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −8.47013 | −0.463465 | ||||||||
\(335\) | −4.85728 | − | 34.5718i | −0.265381 | − | 1.88886i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11.1111i | 0.605259i | 0.953108 | + | 0.302629i | \(0.0978645\pi\) | ||||
−0.953108 | + | 0.302629i | \(0.902136\pi\) | |||||||
\(338\) | 20.7146i | 1.12672i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1.18421 | + | 8.42864i | 0.0642227 | + | 0.457107i | ||||
\(341\) | 11.6128 | 0.628871 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 24.8573i | 1.34217i | ||||||||
\(344\) | −10.9906 | −0.592575 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −22.4701 | −1.20800 | ||||||||
\(347\) | 14.1936i | 0.761951i | 0.924585 | + | 0.380976i | \(0.124412\pi\) | ||||
−0.924585 | + | 0.380976i | \(0.875588\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −32.3684 | −1.73264 | −0.866321 | − | 0.499488i | \(-0.833521\pi\) | ||||
−0.866321 | + | 0.499488i | \(0.833521\pi\) | |||||||
\(350\) | −21.2859 | + | 6.10171i | −1.13778 | + | 0.326150i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.62222i | 0.139765i | ||||||||
\(353\) | − | 11.8064i | − | 0.628393i | −0.949358 | − | 0.314196i | \(-0.898265\pi\) | ||
0.949358 | − | 0.314196i | \(-0.101735\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 34.5718 | − | 4.85728i | 1.83488 | − | 0.257798i | ||||
\(356\) | −12.4286 | −0.658717 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2.94914i | 0.155867i | ||||||||
\(359\) | −10.8287 | −0.571517 | −0.285758 | − | 0.958302i | \(-0.592245\pi\) | ||||
−0.285758 | + | 0.958302i | \(0.592245\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | − | 22.8988i | − | 1.20353i | ||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 25.7146 | 1.34781 | ||||||||
\(365\) | 3.61285 | + | 25.7146i | 0.189105 | + | 1.34596i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 1.46965i | − | 0.0767151i | −0.999264 | − | 0.0383576i | \(-0.987787\pi\) | ||
0.999264 | − | 0.0383576i | \(-0.0122126\pi\) | |||||||
\(368\) | − | 2.62222i | − | 0.136692i | ||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −12.8573 | + | 1.80642i | −0.668418 | + | 0.0939115i | ||||
\(371\) | −26.5718 | −1.37954 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 24.3783i | − | 1.26226i | −0.775678 | − | 0.631129i | \(-0.782592\pi\) | ||
0.775678 | − | 0.631129i | \(-0.217408\pi\) | |||||||
\(374\) | −9.98126 | −0.516119 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.62222 | 0.135230 | ||||||||
\(377\) | − | 19.6128i | − | 1.01011i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −18.9590 | −0.973858 | −0.486929 | − | 0.873442i | \(-0.661883\pi\) | ||||
−0.486929 | + | 0.873442i | \(0.661883\pi\) | |||||||
\(380\) | −2.21432 | + | 0.311108i | −0.113592 | + | 0.0159595i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − | 9.05086i | − | 0.463082i | ||||||
\(383\) | − | 26.1017i | − | 1.33374i | −0.745176 | − | 0.666868i | \(-0.767635\pi\) | ||
0.745176 | − | 0.666868i | \(-0.232365\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.61285 | − | 25.7146i | −0.184128 | − | 1.31054i | ||||
\(386\) | −18.7239 | −0.953023 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − | 7.37778i | − | 0.374550i | ||||||
\(389\) | −3.57136 | −0.181075 | −0.0905376 | − | 0.995893i | \(-0.528859\pi\) | ||||
−0.0905376 | + | 0.995893i | \(0.528859\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.98126 | 0.504774 | ||||||||
\(392\) | − | 12.6128i | − | 0.637045i | ||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −0.888922 | −0.0447832 | ||||||||
\(395\) | 9.80642 | − | 1.37778i | 0.493415 | − | 0.0693239i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 31.4193i | 1.57689i | 0.615107 | + | 0.788444i | \(0.289113\pi\) | ||||
−0.615107 | + | 0.788444i | \(0.710887\pi\) | |||||||
\(398\) | 21.7146i | 1.08845i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4.80642 | − | 1.37778i | 0.240321 | − | 0.0688892i | ||||
\(401\) | −12.0415 | −0.601323 | −0.300662 | − | 0.953731i | \(-0.597207\pi\) | ||||
−0.300662 | + | 0.953731i | \(0.597207\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 25.7146i | 1.28093i | ||||||||
\(404\) | 17.6731 | 0.879268 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −14.9590 | −0.742402 | ||||||||
\(407\) | − | 15.2257i | − | 0.754710i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −26.4701 | −1.30886 | −0.654432 | − | 0.756121i | \(-0.727092\pi\) | ||||
−0.654432 | + | 0.756121i | \(0.727092\pi\) | |||||||
\(410\) | −1.76494 | − | 12.5620i | −0.0871640 | − | 0.620393i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 1.18421i | − | 0.0583418i | ||||||
\(413\) | 4.65386i | 0.229001i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.70471 | − | 26.3684i | −0.181857 | − | 1.29437i | ||||
\(416\) | −5.80642 | −0.284683 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − | 2.62222i | − | 0.128257i | ||||||
\(419\) | −25.9684 | −1.26864 | −0.634319 | − | 0.773072i | \(-0.718719\pi\) | ||||
−0.634319 | + | 0.773072i | \(0.718719\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −29.2672 | −1.42640 | −0.713198 | − | 0.700963i | \(-0.752754\pi\) | ||||
−0.713198 | + | 0.700963i | \(0.752754\pi\) | |||||||
\(422\) | 3.61285i | 0.175871i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 6.00000 | 0.291386 | ||||||||
\(425\) | 5.24443 | + | 18.2953i | 0.254392 | + | 0.887452i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 21.0607i | − | 1.01920i | ||||||
\(428\) | 4.85728i | 0.234785i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −24.3368 | + | 3.41927i | −1.17362 | + | 0.164892i | ||||
\(431\) | −14.8385 | −0.714747 | −0.357374 | − | 0.933961i | \(-0.616328\pi\) | ||||
−0.357374 | + | 0.933961i | \(0.616328\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.27607i | 0.253552i | 0.991931 | + | 0.126776i | \(0.0404629\pi\) | ||||
−0.991931 | + | 0.126776i | \(0.959537\pi\) | |||||||
\(434\) | 19.6128 | 0.941447 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −6.04149 | −0.289335 | ||||||||
\(437\) | 2.62222i | 0.125438i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −31.8578 | −1.52049 | −0.760244 | − | 0.649638i | \(-0.774921\pi\) | ||||
−0.760244 | + | 0.649638i | \(0.774921\pi\) | |||||||
\(440\) | 0.815792 | + | 5.80642i | 0.0388913 | + | 0.276810i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 22.1017i | − | 1.05127i | ||||||
\(443\) | − | 4.94914i | − | 0.235141i | −0.993065 | − | 0.117570i | \(-0.962489\pi\) | ||
0.993065 | − | 0.117570i | \(-0.0375106\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −27.5210 | + | 3.86665i | −1.30462 | + | 0.183297i | ||||
\(446\) | 21.3876 | 1.01273 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 4.42864i | 0.209234i | ||||||||
\(449\) | 9.75605 | 0.460416 | 0.230208 | − | 0.973141i | \(-0.426059\pi\) | ||||
0.230208 | + | 0.973141i | \(0.426059\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 14.8760 | 0.700484 | ||||||||
\(452\) | − | 9.34614i | − | 0.439606i | ||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −8.47013 | −0.397523 | ||||||||
\(455\) | 56.9403 | − | 8.00000i | 2.66940 | − | 0.375046i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.00000i | 0.374224i | 0.982339 | + | 0.187112i | \(0.0599128\pi\) | ||||
−0.982339 | + | 0.187112i | \(0.940087\pi\) | |||||||
\(458\) | − | 16.9590i | − | 0.792442i | ||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −0.815792 | − | 5.80642i | −0.0380365 | − | 0.270726i | ||||
\(461\) | 36.1245 | 1.68248 | 0.841242 | − | 0.540659i | \(-0.181825\pi\) | ||||
0.841242 | + | 0.540659i | \(0.181825\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 35.1209i | − | 1.63221i | −0.577905 | − | 0.816104i | \(-0.696130\pi\) | ||
0.577905 | − | 0.816104i | \(-0.303870\pi\) | |||||||
\(464\) | 3.37778 | 0.156810 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −17.9081 | −0.829578 | ||||||||
\(467\) | 4.56199i | 0.211104i | 0.994414 | + | 0.105552i | \(0.0336609\pi\) | ||||
−0.994414 | + | 0.105552i | \(0.966339\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 69.1437 | 3.19276 | ||||||||
\(470\) | 5.80642 | − | 0.815792i | 0.267830 | − | 0.0376297i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − | 1.05086i | − | 0.0483695i | ||||||
\(473\) | − | 28.8198i | − | 1.32514i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.80642 | + | 1.37778i | −0.220534 | + | 0.0632171i | ||||
\(476\) | −16.8573 | −0.772652 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 28.2766i | 1.29334i | ||||||||
\(479\) | 37.4005 | 1.70887 | 0.854437 | − | 0.519555i | \(-0.173902\pi\) | ||||
0.854437 | + | 0.519555i | \(0.173902\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 33.7146 | 1.53725 | ||||||||
\(482\) | 11.5111i | 0.524318i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4.12399 | 0.187454 | ||||||||
\(485\) | −2.29529 | − | 16.3368i | −0.104224 | − | 0.741815i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 20.9175i | − | 0.947862i | −0.880562 | − | 0.473931i | \(-0.842835\pi\) | ||
0.880562 | − | 0.473931i | \(-0.157165\pi\) | |||||||
\(488\) | 4.75557i | 0.215274i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −3.92396 | − | 27.9289i | −0.177266 | − | 1.26170i | ||||
\(491\) | 15.8666 | 0.716052 | 0.358026 | − | 0.933712i | \(-0.383450\pi\) | ||||
0.358026 | + | 0.933712i | \(0.383450\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 12.8573i | 0.579063i | ||||||||
\(494\) | 5.80642 | 0.261243 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4.42864 | −0.198852 | ||||||||
\(497\) | 69.1437i | 3.10152i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −16.7368 | −0.749244 | −0.374622 | − | 0.927178i | \(-0.622227\pi\) | ||||
−0.374622 | + | 0.927178i | \(0.622227\pi\) | |||||||
\(500\) | 10.2143 | − | 4.54617i | 0.456798 | − | 0.203311i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 7.74620i | − | 0.345730i | ||||||
\(503\) | 21.9684i | 0.979521i | 0.871857 | + | 0.489760i | \(0.162916\pi\) | ||||
−0.871857 | + | 0.489760i | \(0.837084\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 39.1338 | − | 5.49823i | 1.74143 | − | 0.244668i | ||||
\(506\) | 6.87601 | 0.305676 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | − | 6.42864i | − | 0.285225i | ||||||
\(509\) | −15.2573 | −0.676270 | −0.338135 | − | 0.941098i | \(-0.609796\pi\) | ||||
−0.338135 | + | 0.941098i | \(0.609796\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −51.4291 | −2.27509 | ||||||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 13.8796 | 0.612201 | ||||||||
\(515\) | −0.368416 | − | 2.62222i | −0.0162344 | − | 0.115549i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.87601i | 0.302407i | ||||||||
\(518\) | − | 25.7146i | − | 1.12983i | ||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −12.8573 | + | 1.80642i | −0.563829 | + | 0.0792169i | ||||
\(521\) | 18.3269 | 0.802917 | 0.401459 | − | 0.915877i | \(-0.368503\pi\) | ||||
0.401459 | + | 0.915877i | \(0.368503\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 24.8573i | − | 1.08693i | −0.839431 | − | 0.543466i | \(-0.817112\pi\) | ||
0.839431 | − | 0.543466i | \(-0.182888\pi\) | |||||||
\(524\) | −15.0923 | −0.659312 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −18.6222 | −0.811967 | ||||||||
\(527\) | − | 16.8573i | − | 0.734315i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 16.1240 | 0.701043 | ||||||||
\(530\) | 13.2859 | − | 1.86665i | 0.577103 | − | 0.0810820i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | − | 4.42864i | − | 0.192006i | ||||||
\(533\) | 32.9403i | 1.42680i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.51114 | + | 10.7556i | 0.0653322 | + | 0.465004i | ||||
\(536\) | −15.6128 | −0.674372 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 15.8479i | − | 0.683252i | ||||||
\(539\) | 33.0736 | 1.42458 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.34614 | −0.0578751 | −0.0289376 | − | 0.999581i | \(-0.509212\pi\) | ||||
−0.0289376 | + | 0.999581i | \(0.509212\pi\) | |||||||
\(542\) | − | 1.51114i | − | 0.0649089i | ||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 3.80642 | 0.163199 | ||||||||
\(545\) | −13.3778 | + | 1.87955i | −0.573041 | + | 0.0805112i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 8.59057i | − | 0.367306i | −0.982991 | − | 0.183653i | \(-0.941208\pi\) | ||
0.982991 | − | 0.183653i | \(-0.0587923\pi\) | |||||||
\(548\) | − | 7.53972i | − | 0.322081i | ||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 3.61285 | + | 12.6035i | 0.154052 | + | 0.537414i | ||||
\(551\) | −3.37778 | −0.143898 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 19.6128i | 0.834023i | ||||||||
\(554\) | 1.05086 | 0.0446466 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0.387152 | 0.0164189 | ||||||||
\(557\) | 5.86665i | 0.248578i | 0.992246 | + | 0.124289i | \(0.0396650\pi\) | ||||
−0.992246 | + | 0.124289i | \(0.960335\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 63.8163 | 2.69914 | ||||||||
\(560\) | 1.37778 | + | 9.80642i | 0.0582220 | + | 0.414397i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 3.45091i | 0.145568i | ||||||||
\(563\) | 31.4291i | 1.32458i | 0.749248 | + | 0.662290i | \(0.230415\pi\) | ||||
−0.749248 | + | 0.662290i | \(0.769585\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.90766 | − | 20.6953i | −0.122326 | − | 0.870660i | ||||
\(566\) | −15.5812 | −0.654927 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 15.6128i | − | 0.655101i | ||||||
\(569\) | −7.95851 | −0.333638 | −0.166819 | − | 0.985988i | \(-0.553350\pi\) | ||||
−0.166819 | + | 0.985988i | \(0.553350\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −30.8385 | −1.29055 | −0.645276 | − | 0.763949i | \(-0.723258\pi\) | ||||
−0.645276 | + | 0.763949i | \(0.723258\pi\) | |||||||
\(572\) | − | 15.2257i | − | 0.636618i | ||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 25.1240 | 1.04865 | ||||||||
\(575\) | −3.61285 | − | 12.6035i | −0.150666 | − | 0.525601i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 32.0000i | 1.33218i | 0.745873 | + | 0.666089i | \(0.232033\pi\) | ||||
−0.745873 | + | 0.666089i | \(0.767967\pi\) | |||||||
\(578\) | − | 2.51114i | − | 0.104450i | ||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 7.47949 | − | 1.05086i | 0.310569 | − | 0.0436344i | ||||
\(581\) | 52.7368 | 2.18789 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 15.7333i | 0.651606i | ||||||||
\(584\) | 11.6128 | 0.480543 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 7.12399 | 0.294289 | ||||||||
\(587\) | − | 17.8064i | − | 0.734950i | −0.930033 | − | 0.367475i | \(-0.880222\pi\) | ||
0.930033 | − | 0.367475i | \(-0.119778\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.42864 | 0.182479 | ||||||||
\(590\) | −0.326929 | − | 2.32693i | −0.0134595 | − | 0.0957982i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 5.80642i | 0.238643i | ||||||||
\(593\) | − | 13.3176i | − | 0.546887i | −0.961888 | − | 0.273443i | \(-0.911837\pi\) | ||
0.961888 | − | 0.273443i | \(-0.0881626\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −37.3274 | + | 5.24443i | −1.53027 | + | 0.215001i | ||||
\(596\) | 14.5303 | 0.595186 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 15.2257i | 0.622625i | ||||||||
\(599\) | −43.8163 | −1.79028 | −0.895142 | − | 0.445781i | \(-0.852926\pi\) | ||||
−0.895142 | + | 0.445781i | \(0.852926\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9.73329 | −0.397029 | −0.198515 | − | 0.980098i | \(-0.563612\pi\) | ||||
−0.198515 | + | 0.980098i | \(0.563612\pi\) | |||||||
\(602\) | − | 48.6735i | − | 1.98379i | ||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −4.69535 | −0.191051 | ||||||||
\(605\) | 9.13182 | − | 1.28300i | 0.371261 | − | 0.0521615i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 31.9398i | − | 1.29640i | −0.761472 | − | 0.648198i | \(-0.775523\pi\) | ||
0.761472 | − | 0.648198i | \(-0.224477\pi\) | |||||||
\(608\) | 1.00000i | 0.0405554i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.47949 | + | 10.5303i | 0.0599030 | + | 0.426361i | ||||
\(611\) | −15.2257 | −0.615966 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 11.8064i | − | 0.476857i | −0.971160 | − | 0.238428i | \(-0.923368\pi\) | ||
0.971160 | − | 0.238428i | \(-0.0766323\pi\) | |||||||
\(614\) | 1.12399 | 0.0453603 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −11.6128 | −0.467895 | ||||||||
\(617\) | − | 26.5620i | − | 1.06935i | −0.845059 | − | 0.534673i | \(-0.820435\pi\) | ||
0.845059 | − | 0.534673i | \(-0.179565\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −7.34614 | −0.295266 | −0.147633 | − | 0.989042i | \(-0.547166\pi\) | ||||
−0.147633 | + | 0.989042i | \(0.547166\pi\) | |||||||
\(620\) | −9.80642 | + | 1.37778i | −0.393835 | + | 0.0553332i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 14.9491i | 0.599406i | ||||||||
\(623\) | − | 55.0420i | − | 2.20521i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 21.2034 | − | 13.2444i | 0.848137 | − | 0.529777i | ||||
\(626\) | −3.14272 | −0.125608 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 21.5210i | 0.858781i | ||||||||
\(629\) | −22.1017 | −0.881253 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −30.7556 | −1.22436 | −0.612180 | − | 0.790718i | \(-0.709707\pi\) | ||||
−0.612180 | + | 0.790718i | \(0.709707\pi\) | |||||||
\(632\) | − | 4.42864i | − | 0.176162i | ||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −10.5906 | −0.420605 | ||||||||
\(635\) | −2.00000 | − | 14.2351i | −0.0793676 | − | 0.564901i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 73.2355i | 2.90170i | ||||||||
\(638\) | 8.85728i | 0.350663i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −0.311108 | − | 2.21432i | −0.0122976 | − | 0.0875287i | ||||
\(641\) | 39.3876 | 1.55572 | 0.777859 | − | 0.628439i | \(-0.216306\pi\) | ||||
0.777859 | + | 0.628439i | \(0.216306\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 24.1146i | − | 0.950988i | −0.879719 | − | 0.475494i | \(-0.842269\pi\) | ||
0.879719 | − | 0.475494i | \(-0.157731\pi\) | |||||||
\(644\) | 11.6128 | 0.457610 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3.80642 | −0.149762 | ||||||||
\(647\) | 47.6829i | 1.87461i | 0.348512 | + | 0.937304i | \(0.386687\pi\) | ||||
−0.348512 | + | 0.937304i | \(0.613313\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.75557 | 0.108166 | ||||||||
\(650\) | −27.9081 | + | 8.00000i | −1.09465 | + | 0.313786i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − | 8.23506i | − | 0.322510i | ||||||
\(653\) | 21.7462i | 0.850995i | 0.904960 | + | 0.425497i | \(0.139901\pi\) | ||||
−0.904960 | + | 0.425497i | \(0.860099\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −33.4193 | + | 4.69535i | −1.30580 | + | 0.183462i | ||||
\(656\) | −5.67307 | −0.221496 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 11.6128i | 0.452716i | ||||||||
\(659\) | −16.1936 | −0.630812 | −0.315406 | − | 0.948957i | \(-0.602141\pi\) | ||||
−0.315406 | + | 0.948957i | \(0.602141\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −22.5116 | −0.875600 | −0.437800 | − | 0.899072i | \(-0.644242\pi\) | ||||
−0.437800 | + | 0.899072i | \(0.644242\pi\) | |||||||
\(662\) | 15.1427i | 0.588539i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −11.9081 | −0.462125 | ||||||||
\(665\) | −1.37778 | − | 9.80642i | −0.0534282 | − | 0.380277i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 8.85728i | − | 0.342955i | ||||||
\(668\) | 8.47013i | 0.327719i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −34.5718 | + | 4.85728i | −1.33563 | + | 0.187653i | ||||
\(671\) | −12.4701 | −0.481404 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 9.66323i | − | 0.372490i | −0.982503 | − | 0.186245i | \(-0.940368\pi\) | ||
0.982503 | − | 0.186245i | \(-0.0596318\pi\) | |||||||
\(674\) | 11.1111 | 0.427983 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 20.7146 | 0.796714 | ||||||||
\(677\) | 6.85728i | 0.263547i | 0.991280 | + | 0.131773i | \(0.0420671\pi\) | ||||
−0.991280 | + | 0.131773i | \(0.957933\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 32.6735 | 1.25390 | ||||||||
\(680\) | 8.42864 | − | 1.18421i | 0.323224 | − | 0.0454123i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − | 11.6128i | − | 0.444679i | ||||||
\(683\) | 30.3051i | 1.15959i | 0.814761 | + | 0.579797i | \(0.196868\pi\) | ||||
−0.814761 | + | 0.579797i | \(0.803132\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.34567 | − | 16.6953i | −0.0896233 | − | 0.637896i | ||||
\(686\) | 24.8573 | 0.949055 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 10.9906i | 0.419014i | ||||||||
\(689\) | −34.8385 | −1.32724 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.61285 | 0.289606 | 0.144803 | − | 0.989460i | \(-0.453745\pi\) | ||||
0.144803 | + | 0.989460i | \(0.453745\pi\) | |||||||
\(692\) | 22.4701i | 0.854186i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 14.1936 | 0.538781 | ||||||||
\(695\) | 0.857279 | − | 0.120446i | 0.0325184 | − | 0.00456878i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 21.5941i | − | 0.817935i | ||||||
\(698\) | 32.3684i | 1.22516i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 6.10171 | + | 21.2859i | 0.230623 | + | 0.804532i | ||||
\(701\) | 32.3654 | 1.22242 | 0.611211 | − | 0.791467i | \(-0.290683\pi\) | ||||
0.611211 | + | 0.791467i | \(0.290683\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 5.80642i | − | 0.218993i | ||||||
\(704\) | 2.62222 | 0.0988285 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −11.8064 | −0.444341 | ||||||||
\(707\) | 78.2677i | 2.94356i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 49.8992 | 1.87401 | 0.937003 | − | 0.349322i | \(-0.113588\pi\) | ||||
0.937003 | + | 0.349322i | \(0.113588\pi\) | |||||||
\(710\) | −4.85728 | − | 34.5718i | −0.182290 | − | 1.29746i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 12.4286i | 0.465783i | ||||||||
\(713\) | 11.6128i | 0.434905i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.73683 | − | 33.7146i | −0.177148 | − | 1.26085i | ||||
\(716\) | 2.94914 | 0.110215 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 10.8287i | 0.404123i | ||||||||
\(719\) | −26.4415 | −0.986103 | −0.493052 | − | 0.870000i | \(-0.664119\pi\) | ||||
−0.493052 | + | 0.870000i | \(0.664119\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.24443 | 0.195313 | ||||||||
\(722\) | − | 1.00000i | − | 0.0372161i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −22.8988 | −0.851026 | ||||||||
\(725\) | 16.2351 | − | 4.65386i | 0.602955 | − | 0.172840i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 48.1245i | 1.78484i | 0.451208 | + | 0.892419i | \(0.350993\pi\) | ||||
−0.451208 | + | 0.892419i | \(0.649007\pi\) | |||||||
\(728\) | − | 25.7146i | − | 0.953045i | ||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 25.7146 | − | 3.61285i | 0.951738 | − | 0.133717i | ||||
\(731\) | −41.8350 | −1.54732 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 14.0286i | 0.518157i | 0.965856 | + | 0.259079i | \(0.0834189\pi\) | ||||
−0.965856 | + | 0.259079i | \(0.916581\pi\) | |||||||
\(734\) | −1.46965 | −0.0542458 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.62222 | −0.0966562 | ||||||||
\(737\) | − | 40.9403i | − | 1.50805i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −10.1847 | −0.374650 | −0.187325 | − | 0.982298i | \(-0.559982\pi\) | ||||
−0.187325 | + | 0.982298i | \(0.559982\pi\) | |||||||
\(740\) | 1.80642 | + | 12.8573i | 0.0664055 | + | 0.472643i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 26.5718i | 0.975483i | ||||||||
\(743\) | − | 42.9590i | − | 1.57601i | −0.615667 | − | 0.788006i | \(-0.711113\pi\) | ||
0.615667 | − | 0.788006i | \(-0.288887\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 32.1748 | − | 4.52051i | 1.17879 | − | 0.165619i | ||||
\(746\) | −24.3783 | −0.892552 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 9.98126i | 0.364951i | ||||||||
\(749\) | −21.5111 | −0.786000 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.18421 | −0.262155 | −0.131078 | − | 0.991372i | \(-0.541844\pi\) | ||||
−0.131078 | + | 0.991372i | \(0.541844\pi\) | |||||||
\(752\) | − | 2.62222i | − | 0.0956224i | ||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −19.6128 | −0.714258 | ||||||||
\(755\) | −10.3970 | + | 1.46076i | −0.378385 | + | 0.0531625i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 41.2543i | 1.49941i | 0.661771 | + | 0.749706i | \(0.269805\pi\) | ||||
−0.661771 | + | 0.749706i | \(0.730195\pi\) | |||||||
\(758\) | 18.9590i | 0.688621i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0.311108 | + | 2.21432i | 0.0112851 | + | 0.0803218i | ||||
\(761\) | −44.3051 | −1.60606 | −0.803030 | − | 0.595939i | \(-0.796780\pi\) | ||||
−0.803030 | + | 0.595939i | \(0.796780\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 26.7556i | − | 0.968617i | ||||||
\(764\) | −9.05086 | −0.327448 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −26.1017 | −0.943093 | ||||||||
\(767\) | 6.10171i | 0.220320i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 6.59057 | 0.237662 | 0.118831 | − | 0.992914i | \(-0.462085\pi\) | ||||
0.118831 | + | 0.992914i | \(0.462085\pi\) | |||||||
\(770\) | −25.7146 | + | 3.61285i | −0.926688 | + | 0.130198i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 18.7239i | 0.673889i | ||||||||
\(773\) | − | 8.83854i | − | 0.317900i | −0.987287 | − | 0.158950i | \(-0.949189\pi\) | ||
0.987287 | − | 0.158950i | \(-0.0508109\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −21.2859 | + | 6.10171i | −0.764613 | + | 0.219180i | ||||
\(776\) | −7.37778 | −0.264847 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 3.57136i | 0.128039i | ||||||||
\(779\) | 5.67307 | 0.203259 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 40.9403 | 1.46496 | ||||||||
\(782\) | − | 9.98126i | − | 0.356929i | ||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −12.6128 | −0.450459 | ||||||||
\(785\) | 6.69535 | + | 47.6543i | 0.238967 | + | 1.70086i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 16.9403i | − | 0.603855i | −0.953331 | − | 0.301927i | \(-0.902370\pi\) | ||
0.953331 | − | 0.301927i | \(-0.0976300\pi\) | |||||||
\(788\) | 0.888922i | 0.0316665i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −1.37778 | − | 9.80642i | −0.0490194 | − | 0.348897i | ||||
\(791\) | 41.3907 | 1.47168 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 27.6128i | − | 0.980561i | ||||||
\(794\) | 31.4193 | 1.11503 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 21.7146 | 0.769652 | ||||||||
\(797\) | 40.1847i | 1.42341i | 0.702476 | + | 0.711707i | \(0.252078\pi\) | ||||
−0.702476 | + | 0.711707i | \(0.747922\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.98126 | 0.353112 | ||||||||
\(800\) | −1.37778 | − | 4.80642i | −0.0487120 | − | 0.169933i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 12.0415i | 0.425200i | ||||||||
\(803\) | 30.4514i | 1.07461i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 25.7146 | − | 3.61285i | 0.906319 | − | 0.127336i | ||||
\(806\) | 25.7146 | 0.905757 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − | 17.6731i | − | 0.621736i | ||||||
\(809\) | 29.1052 | 1.02329 | 0.511643 | − | 0.859198i | \(-0.329037\pi\) | ||||
0.511643 | + | 0.859198i | \(0.329037\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 38.7753 | 1.36158 | 0.680792 | − | 0.732477i | \(-0.261636\pi\) | ||||
0.680792 | + | 0.732477i | \(0.261636\pi\) | |||||||
\(812\) | 14.9590i | 0.524958i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −15.2257 | −0.533660 | ||||||||
\(815\) | −2.56199 | − | 18.2351i | −0.0897427 | − | 0.638746i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 10.9906i | − | 0.384514i | ||||||
\(818\) | 26.4701i | 0.925506i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −12.5620 | + | 1.76494i | −0.438684 | + | 0.0616343i | ||||
\(821\) | −2.53035 | −0.0883098 | −0.0441549 | − | 0.999025i | \(-0.514060\pi\) | ||||
−0.0441549 | + | 0.999025i | \(0.514060\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 24.0415i | 0.838034i | 0.907978 | + | 0.419017i | \(0.137625\pi\) | ||||
−0.907978 | + | 0.419017i | \(0.862375\pi\) | |||||||
\(824\) | −1.18421 | −0.0412538 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 4.65386 | 0.161928 | ||||||||
\(827\) | 6.57184i | 0.228525i | 0.993451 | + | 0.114263i | \(0.0364505\pi\) | ||||
−0.993451 | + | 0.114263i | \(0.963549\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 28.7338 | 0.997965 | 0.498983 | − | 0.866612i | \(-0.333707\pi\) | ||||
0.498983 | + | 0.866612i | \(0.333707\pi\) | |||||||
\(830\) | −26.3684 | + | 3.70471i | −0.915261 | + | 0.128592i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 5.80642i | 0.201302i | ||||||||
\(833\) | − | 48.0098i | − | 1.66344i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.63512 | + | 18.7556i | 0.0911922 | + | 0.649063i | ||||
\(836\) | −2.62222 | −0.0906912 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 25.9684i | 0.897062i | ||||||||
\(839\) | −50.5718 | −1.74593 | −0.872967 | − | 0.487780i | \(-0.837807\pi\) | ||||
−0.872967 | + | 0.487780i | \(0.837807\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −17.5906 | −0.606571 | ||||||||
\(842\) | 29.2672i | 1.00861i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 3.61285 | 0.124359 | ||||||||
\(845\) | 45.8687 | − | 6.44446i | 1.57793 | − | 0.221696i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 18.2636i | 0.627546i | ||||||||
\(848\) | − | 6.00000i | − | 0.206041i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 18.2953 | − | 5.24443i | 0.627523 | − | 0.179883i | ||||
\(851\) | 15.2257 | 0.521930 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 31.2355i | 1.06948i | 0.845015 | + | 0.534742i | \(0.179591\pi\) | ||||
−0.845015 | + | 0.534742i | \(0.820409\pi\) | |||||||
\(854\) | −21.0607 | −0.720682 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 4.85728 | 0.166018 | ||||||||
\(857\) | − | 27.3274i | − | 0.933486i | −0.884393 | − | 0.466743i | \(-0.845427\pi\) | ||
0.884393 | − | 0.466743i | \(-0.154573\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 34.7753 | 1.18652 | 0.593258 | − | 0.805012i | \(-0.297841\pi\) | ||||
0.593258 | + | 0.805012i | \(0.297841\pi\) | |||||||
\(860\) | 3.41927 | + | 24.3368i | 0.116596 | + | 0.829877i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 14.8385i | 0.505403i | ||||||||
\(863\) | 21.2444i | 0.723169i | 0.932339 | + | 0.361584i | \(0.117764\pi\) | ||||
−0.932339 | + | 0.361584i | \(0.882236\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.99063 | + | 49.7560i | 0.237689 | + | 1.69176i | ||||
\(866\) | 5.27607 | 0.179288 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | − | 19.6128i | − | 0.665703i | ||||||
\(869\) | 11.6128 | 0.393939 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 90.6548 | 3.07172 | ||||||||
\(872\) | 6.04149i | 0.204591i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 2.62222 | 0.0886978 | ||||||||
\(875\) | 20.1334 | + | 45.2355i | 0.680632 | + | 1.52924i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 22.3970i | 0.756293i | 0.925746 | + | 0.378146i | \(0.123438\pi\) | ||||
−0.925746 | + | 0.378146i | \(0.876562\pi\) | |||||||
\(878\) | 31.8578i | 1.07515i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 5.80642 | − | 0.815792i | 0.195735 | − | 0.0275003i | ||||
\(881\) | 20.3684 | 0.686229 | 0.343115 | − | 0.939294i | \(-0.388518\pi\) | ||||
0.343115 | + | 0.939294i | \(0.388518\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 21.6829i | − | 0.729688i | −0.931069 | − | 0.364844i | \(-0.881122\pi\) | ||
0.931069 | − | 0.364844i | \(-0.118878\pi\) | |||||||
\(884\) | −22.1017 | −0.743361 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −4.94914 | −0.166270 | ||||||||
\(887\) | 7.14272i | 0.239829i | 0.992784 | + | 0.119915i | \(0.0382621\pi\) | ||||
−0.992784 | + | 0.119915i | \(0.961738\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 28.4701 | 0.954857 | ||||||||
\(890\) | 3.86665 | + | 27.5210i | 0.129610 | + | 0.922505i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − | 21.3876i | − | 0.716111i | ||||||
\(893\) | 2.62222i | 0.0877491i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.53035 | − | 0.917502i | 0.218286 | − | 0.0306687i | ||||
\(896\) | 4.42864 | 0.147950 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | − | 9.75605i | − | 0.325563i | ||||||
\(899\) | −14.9590 | −0.498910 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 22.8385 | 0.760862 | ||||||||
\(902\) | − | 14.8760i | − | 0.495317i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −9.34614 | −0.310848 | ||||||||
\(905\) | −50.7052 | + | 7.12399i | −1.68550 | + | 0.236809i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 15.3461i | 0.509560i | 0.966999 | + | 0.254780i | \(0.0820031\pi\) | ||||
−0.966999 | + | 0.254780i | \(0.917997\pi\) | |||||||
\(908\) | 8.47013i | 0.281091i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −8.00000 | − | 56.9403i | −0.265197 | − | 1.88755i | ||||
\(911\) | −12.1204 | −0.401568 | −0.200784 | − | 0.979636i | \(-0.564349\pi\) | ||||
−0.200784 | + | 0.979636i | \(0.564349\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 31.2257i | − | 1.03342i | ||||||
\(914\) | 8.00000 | 0.264616 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −16.9590 | −0.560341 | ||||||||
\(917\) | − | 66.8385i | − | 2.20720i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 12.2667 | 0.404641 | 0.202321 | − | 0.979319i | \(-0.435152\pi\) | ||||
0.202321 | + | 0.979319i | \(0.435152\pi\) | |||||||
\(920\) | −5.80642 | + | 0.815792i | −0.191432 | + | 0.0268959i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − | 36.1245i | − | 1.18970i | ||||||
\(923\) | 90.6548i | 2.98394i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.00000 | + | 27.9081i | 0.263038 | + | 0.917614i | ||||
\(926\) | −35.1209 | −1.15415 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | − | 3.37778i | − | 0.110881i | ||||||
\(929\) | −40.1847 | −1.31842 | −0.659208 | − | 0.751960i | \(-0.729108\pi\) | ||||
−0.659208 | + | 0.751960i | \(0.729108\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 12.6128 | 0.413369 | ||||||||
\(932\) | 17.9081i | 0.586600i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 4.56199 | 0.149273 | ||||||||
\(935\) | 3.10525 | + | 22.1017i | 0.101553 | + | 0.722803i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 24.7368i | − | 0.808117i | −0.914733 | − | 0.404059i | \(-0.867599\pi\) | ||
0.914733 | − | 0.404059i | \(-0.132401\pi\) | |||||||
\(938\) | − | 69.1437i | − | 2.25762i | ||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −0.815792 | − | 5.80642i | −0.0266082 | − | 0.189385i | ||||
\(941\) | 1.66323 | 0.0542196 | 0.0271098 | − | 0.999632i | \(-0.491370\pi\) | ||||
0.0271098 | + | 0.999632i | \(0.491370\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 14.8760i | 0.484430i | ||||||||
\(944\) | −1.05086 | −0.0342024 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −28.8198 | −0.937013 | ||||||||
\(947\) | − | 14.8671i | − | 0.483117i | −0.970386 | − | 0.241558i | \(-0.922341\pi\) | ||
0.970386 | − | 0.241558i | \(-0.0776585\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −67.4291 | −2.18884 | ||||||||
\(950\) | 1.37778 | + | 4.80642i | 0.0447012 | + | 0.155941i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 16.8573i | 0.546348i | ||||||||
\(953\) | − | 8.83854i | − | 0.286308i | −0.989700 | − | 0.143154i | \(-0.954275\pi\) | ||
0.989700 | − | 0.143154i | \(-0.0457245\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −20.0415 | + | 2.81579i | −0.648527 | + | 0.0911169i | ||||
\(956\) | 28.2766 | 0.914529 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 37.4005i | − | 1.20836i | ||||||
\(959\) | 33.3907 | 1.07824 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −11.3872 | −0.367327 | ||||||||
\(962\) | − | 33.7146i | − | 1.08700i | ||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 11.5111 | 0.370749 | ||||||||
\(965\) | 5.82516 | + | 41.4608i | 0.187519 | + | 1.33467i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.55262i | 0.0499290i | 0.999688 | + | 0.0249645i | \(0.00794728\pi\) | ||||
−0.999688 | + | 0.0249645i | \(0.992053\pi\) | |||||||
\(968\) | − | 4.12399i | − | 0.132550i | ||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −16.3368 | + | 2.29529i | −0.524542 | + | 0.0736972i | ||||
\(971\) | −44.5433 | −1.42946 | −0.714731 | − | 0.699400i | \(-0.753451\pi\) | ||||
−0.714731 | + | 0.699400i | \(0.753451\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.71456i | 0.0549662i | ||||||||
\(974\) | −20.9175 | −0.670240 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4.75557 | 0.152222 | ||||||||
\(977\) | − | 15.8350i | − | 0.506607i | −0.967387 | − | 0.253303i | \(-0.918483\pi\) | ||
0.967387 | − | 0.253303i | \(-0.0815171\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −32.5906 | −1.04160 | ||||||||
\(980\) | −27.9289 | + | 3.92396i | −0.892155 | + | 0.125346i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − | 15.8666i | − | 0.506325i | ||||||
\(983\) | 6.87601i | 0.219311i | 0.993970 | + | 0.109655i | \(0.0349747\pi\) | ||||
−0.993970 | + | 0.109655i | \(0.965025\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.276551 | + | 1.96836i | 0.00881163 | + | 0.0627171i | ||||
\(986\) | 12.8573 | 0.409459 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − | 5.80642i | − | 0.184727i | ||||||
\(989\) | 28.8198 | 0.916417 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −29.8765 | −0.949058 | −0.474529 | − | 0.880240i | \(-0.657382\pi\) | ||||
−0.474529 | + | 0.880240i | \(0.657382\pi\) | |||||||
\(992\) | 4.42864i | 0.140609i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 69.1437 | 2.19310 | ||||||||
\(995\) | 48.0830 | − | 6.75557i | 1.52433 | − | 0.214166i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.90813i | 0.187112i | 0.995614 | + | 0.0935562i | \(0.0298235\pi\) | ||||
−0.995614 | + | 0.0935562i | \(0.970177\pi\) | |||||||
\(998\) | 16.7368i | 0.529795i | ||||||||
\(999\) | 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 | 1710.2.d.f.1369.1 | 6 | ||
3.2 | odd | 2 | 570.2.d.c.229.6 | yes | 6 | ||
5.2 | odd | 4 | 8550.2.a.cq.1.3 | 3 | |||
5.3 | odd | 4 | 8550.2.a.ce.1.1 | 3 | |||
5.4 | even | 2 | inner | 1710.2.d.f.1369.4 | 6 | ||
15.2 | even | 4 | 2850.2.a.bl.1.3 | 3 | |||
15.8 | even | 4 | 2850.2.a.bm.1.1 | 3 | |||
15.14 | odd | 2 | 570.2.d.c.229.3 | ✓ | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
570.2.d.c.229.3 | ✓ | 6 | 15.14 | odd | 2 | ||
570.2.d.c.229.6 | yes | 6 | 3.2 | odd | 2 | ||
1710.2.d.f.1369.1 | 6 | 1.1 | even | 1 | trivial | ||
1710.2.d.f.1369.4 | 6 | 5.4 | even | 2 | inner | ||
2850.2.a.bl.1.3 | 3 | 15.2 | even | 4 | |||
2850.2.a.bm.1.1 | 3 | 15.8 | even | 4 | |||
8550.2.a.ce.1.1 | 3 | 5.3 | odd | 4 | |||
8550.2.a.cq.1.3 | 3 | 5.2 | odd | 4 |