Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3584,2,Mod(1793,3584)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3584, 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("3584.1793");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3584 = 2^{9} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3584.b (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(28.6183840844\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 4 x^{11} + 4 x^{10} + 8 x^{9} - 24 x^{8} + 24 x^{7} + 176 x^{6} + 160 x^{5} + 145 x^{4} + 108 x^{3} + 68 x^{2} + 32 x + 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{14} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1793.6 | ||
Root | \(0.271901 + 0.656426i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3584.1793 |
Dual form | 3584.2.b.i.1793.7 |
$q$-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 \(\left(\mathbb{Z}/3584\mathbb{Z}\right)^\times\).
\(n\) | \(1023\) | \(1025\) | \(1541\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − 0.101362i | − 0.0585211i | −0.999572 | − | 0.0292606i | \(-0.990685\pi\) | ||||
0.999572 | − | 0.0292606i | \(-0.00931526\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.19640i | 0.982260i | 0.871086 | + | 0.491130i | \(0.163416\pi\) | ||||
−0.871086 | + | 0.491130i | \(0.836584\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.98973 | 0.996575 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 0.674013i | − 0.203223i | −0.994824 | − | 0.101611i | \(-0.967600\pi\) | ||||
0.994824 | − | 0.101611i | \(-0.0323998\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.30258i | 1.47067i | 0.677704 | + | 0.735335i | \(0.262975\pi\) | ||||
−0.677704 | + | 0.735335i | \(0.737025\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.222631 | 0.0574830 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.87523 | 0.939881 | 0.469941 | − | 0.882698i | \(-0.344275\pi\) | ||||
0.469941 | + | 0.882698i | \(0.344275\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.995183i | 0.228311i | 0.993463 | + | 0.114155i | \(0.0364162\pi\) | ||||
−0.993463 | + | 0.114155i | \(0.963584\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.101362i | 0.0221189i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.36590 | 0.701840 | 0.350920 | − | 0.936406i | \(-0.385869\pi\) | ||||
0.350920 | + | 0.936406i | \(0.385869\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.175829 | 0.0351657 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 0.607128i | − 0.116842i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 0.134404i | − 0.0249582i | −0.999922 | − | 0.0124791i | \(-0.996028\pi\) | ||||
0.999922 | − | 0.0124791i | \(-0.00397233\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.11512 | −0.559492 | −0.279746 | − | 0.960074i | \(-0.590250\pi\) | ||||
−0.279746 | + | 0.960074i | \(0.590250\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.0683190 | −0.0118928 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 2.19640i | − 0.371259i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.07795i | 0.341613i | 0.985305 | + | 0.170807i | \(0.0546373\pi\) | ||||
−0.985305 | + | 0.170807i | \(0.945363\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.537478 | 0.0860653 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.76710 | 0.588321 | 0.294161 | − | 0.955756i | \(-0.404960\pi\) | ||||
0.294161 | + | 0.955756i | \(0.404960\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 3.61268i | − 0.550929i | −0.961311 | − | 0.275464i | \(-0.911168\pi\) | ||||
0.961311 | − | 0.275464i | \(-0.0888316\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 6.56663i | 0.978896i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.68913 | −0.975709 | −0.487855 | − | 0.872925i | \(-0.662220\pi\) | ||||
−0.487855 | + | 0.872925i | \(0.662220\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − 0.392799i | − 0.0550029i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.93656i | 0.403368i | 0.979451 | + | 0.201684i | \(0.0646413\pi\) | ||||
−0.979451 | + | 0.201684i | \(0.935359\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.48040 | 0.199617 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.100873 | 0.0133610 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 6.92085i | − 0.901017i | −0.892772 | − | 0.450509i | \(-0.851243\pi\) | ||||
0.892772 | − | 0.450509i | \(-0.148757\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 4.30265i | − 0.550898i | −0.961316 | − | 0.275449i | \(-0.911173\pi\) | ||||
0.961316 | − | 0.275449i | \(-0.0888265\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.98973 | −0.376670 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −11.6466 | −1.44458 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 13.9311i | 1.70196i | 0.525198 | + | 0.850980i | \(0.323991\pi\) | ||||
−0.525198 | + | 0.850980i | \(0.676009\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 0.341173i | − 0.0410724i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.6460 | 1.26344 | 0.631721 | − | 0.775196i | \(-0.282349\pi\) | ||||
0.631721 | + | 0.775196i | \(0.282349\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.62368 | −1.00932 | −0.504662 | − | 0.863317i | \(-0.668383\pi\) | ||||
−0.504662 | + | 0.863317i | \(0.668383\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − 0.0178223i | − 0.00205794i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.674013i | 0.0768109i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.12273 | 0.801369 | 0.400685 | − | 0.916216i | \(-0.368772\pi\) | ||||
0.400685 | + | 0.916216i | \(0.368772\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.90764 | 0.989738 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 15.1833i | 1.66658i | 0.552834 | + | 0.833291i | \(0.313546\pi\) | ||||
−0.552834 | + | 0.833291i | \(0.686454\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.51155i | 0.923207i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.0136234 | −0.00146058 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.856726 | −0.0908128 | −0.0454064 | − | 0.998969i | \(-0.514458\pi\) | ||||
−0.0454064 | + | 0.998969i | \(0.514458\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 5.30258i | − 0.555861i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.315754i | 0.0327421i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.18582 | −0.224260 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −11.0125 | −1.11815 | −0.559074 | − | 0.829118i | \(-0.688843\pi\) | ||||
−0.559074 | + | 0.829118i | \(0.688843\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − 2.01511i | − 0.202527i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.354276i | 0.0352518i | 0.999845 | + | 0.0176259i | \(0.00561079\pi\) | ||||
−0.999845 | + | 0.0176259i | \(0.994389\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −16.5750 | −1.63318 | −0.816590 | − | 0.577218i | \(-0.804138\pi\) | ||||
−0.816590 | + | 0.577218i | \(0.804138\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.222631 | −0.0217265 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 17.7782i | − 1.71869i | −0.511400 | − | 0.859343i | \(-0.670873\pi\) | ||||
0.511400 | − | 0.859343i | \(-0.329127\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.1967i | 0.976667i | 0.872657 | + | 0.488334i | \(0.162395\pi\) | ||||
−0.872657 | + | 0.488334i | \(0.837605\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.210624 | 0.0199916 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.69262 | 0.911805 | 0.455902 | − | 0.890030i | \(-0.349317\pi\) | ||||
0.455902 | + | 0.890030i | \(0.349317\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.39287i | 0.689389i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 15.8533i | 1.46563i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.87523 | −0.355242 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.5457 | 0.958701 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 0.381839i | − 0.0344292i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.3682i | 1.01680i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 20.2674 | 1.79844 | 0.899220 | − | 0.437497i | \(-0.144135\pi\) | ||||
0.899220 | + | 0.437497i | \(0.144135\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.366187 | −0.0322410 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 17.8643i | 1.56081i | 0.625272 | + | 0.780406i | \(0.284988\pi\) | ||||
−0.625272 | + | 0.780406i | \(0.715012\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 0.995183i | − 0.0862933i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.33350 | 0.114769 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −11.4894 | −0.981606 | −0.490803 | − | 0.871271i | \(-0.663296\pi\) | ||||
−0.490803 | + | 0.871271i | \(0.663296\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 0.209585i | − 0.0177768i | −0.999960 | − | 0.00888838i | \(-0.997171\pi\) | ||||
0.999960 | − | 0.00888838i | \(-0.00282929\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.678020i | 0.0570996i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.57401 | 0.298873 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.295205 | 0.0245155 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 0.101362i | − 0.00836016i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 10.5895i | 0.867526i | 0.901027 | + | 0.433763i | \(0.142814\pi\) | ||||
−0.901027 | + | 0.433763i | \(0.857186\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.4820 | −0.934391 | −0.467196 | − | 0.884154i | \(-0.654736\pi\) | ||||
−0.467196 | + | 0.884154i | \(0.654736\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 11.5859 | 0.936662 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 6.84205i | − 0.549567i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.98207i | 0.796656i | 0.917243 | + | 0.398328i | \(0.130409\pi\) | ||||
−0.917243 | + | 0.398328i | \(0.869591\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.297654 | 0.0236055 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.36590 | −0.265270 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 3.76859i | − 0.295178i | −0.989049 | − | 0.147589i | \(-0.952849\pi\) | ||||
0.989049 | − | 0.147589i | \(-0.0471513\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − 0.150056i | − 0.0116818i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −8.45888 | −0.654568 | −0.327284 | − | 0.944926i | \(-0.606133\pi\) | ||||
−0.327284 | + | 0.944926i | \(0.606133\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −15.1173 | −1.16287 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.97533i | 0.227529i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 1.41548i | − 0.107617i | −0.998551 | − | 0.0538085i | \(-0.982864\pi\) | ||||
0.998551 | − | 0.0538085i | \(-0.0171361\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.175829 | −0.0132914 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.701508 | −0.0527286 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 17.2449i | − 1.28894i | −0.764629 | − | 0.644470i | \(-0.777078\pi\) | ||||
0.764629 | − | 0.644470i | \(-0.222922\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 4.77705i | − 0.355075i | −0.984114 | − | 0.177538i | \(-0.943187\pi\) | ||||
0.984114 | − | 0.177538i | \(-0.0568132\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.436123 | −0.0322392 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.56401 | −0.335553 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 2.61195i | − 0.191005i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.607128i | 0.0441621i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.90148 | −0.644089 | −0.322044 | − | 0.946725i | \(-0.604370\pi\) | ||||
−0.322044 | + | 0.946725i | \(0.604370\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.9910 | −0.863129 | −0.431565 | − | 0.902082i | \(-0.642038\pi\) | ||||
−0.431565 | + | 0.902082i | \(0.642038\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.18052i | 0.0845385i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 18.5079i | 1.31863i | 0.751865 | + | 0.659317i | \(0.229154\pi\) | ||||
−0.751865 | + | 0.659317i | \(0.770846\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.13252 | 0.151170 | 0.0755852 | − | 0.997139i | \(-0.475918\pi\) | ||||
0.0755852 | + | 0.997139i | \(0.475918\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.41208 | 0.0996006 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.134404i | 0.00943332i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8.27405i | 0.577884i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 10.0631 | 0.699436 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.670766 | 0.0463979 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 22.7237i | 1.56436i | 0.623051 | + | 0.782181i | \(0.285893\pi\) | ||||
−0.623051 | + | 0.782181i | \(0.714107\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 1.07909i | − 0.0739381i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 7.93489 | 0.541155 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.11512 | 0.211468 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.874109i | 0.0590668i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 20.5487i | 1.38226i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.10025 | −0.0736781 | −0.0368391 | − | 0.999321i | \(-0.511729\pi\) | ||||
−0.0368391 | + | 0.999321i | \(0.511729\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.525679 | 0.0350453 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 2.63939i | − 0.175183i | −0.996156 | − | 0.0875913i | \(-0.972083\pi\) | ||||
0.996156 | − | 0.0875913i | \(-0.0279169\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 19.2282i | 1.27064i | 0.772250 | + | 0.635319i | \(0.219131\pi\) | ||||
−0.772250 | + | 0.635319i | \(0.780869\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.0683190 | 0.00449506 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −8.69975 | −0.569939 | −0.284970 | − | 0.958537i | \(-0.591984\pi\) | ||||
−0.284970 | + | 0.958537i | \(0.591984\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 14.6920i | − 0.958400i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 0.721971i | − 0.0468970i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.72852 | −0.111809 | −0.0559044 | − | 0.998436i | \(-0.517804\pi\) | ||||
−0.0559044 | + | 0.998436i | \(0.517804\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 17.6482 | 1.13682 | 0.568409 | − | 0.822746i | \(-0.307559\pi\) | ||||
0.568409 | + | 0.822746i | \(0.307559\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 2.72428i | − 0.174762i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.19640i | 0.140323i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.27704 | −0.335770 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.53900 | 0.0975303 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 14.6099i | 0.922169i | 0.887356 | + | 0.461084i | \(0.152539\pi\) | ||||
−0.887356 | + | 0.461084i | \(0.847461\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 2.26866i | − 0.142630i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.862744 | 0.0540271 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −24.1929 | −1.50911 | −0.754556 | − | 0.656235i | \(-0.772148\pi\) | ||||
−0.754556 | + | 0.656235i | \(0.772148\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 2.07795i | − 0.129118i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − 0.401832i | − 0.0248727i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 23.8158 | 1.46854 | 0.734271 | − | 0.678856i | \(-0.237524\pi\) | ||||
0.734271 | + | 0.678856i | \(0.237524\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.44986 | −0.396212 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.0868391i | 0.00531446i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0.304478i | 0.0185643i | 0.999957 | + | 0.00928216i | \(0.00295465\pi\) | ||||
−0.999957 | + | 0.00928216i | \(0.997045\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −17.2018 | −1.04493 | −0.522467 | − | 0.852659i | \(-0.674988\pi\) | ||||
−0.522467 | + | 0.852659i | \(0.674988\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.537478 | −0.0325296 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 0.118511i | − 0.00714646i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 21.1489i | − 1.27072i | −0.772218 | − | 0.635358i | \(-0.780853\pi\) | ||||
0.772218 | − | 0.635358i | \(-0.219147\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −9.31336 | −0.557576 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −11.0974 | −0.662018 | −0.331009 | − | 0.943628i | \(-0.607389\pi\) | ||||
−0.331009 | + | 0.943628i | \(0.607389\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 23.8050i | − 1.41506i | −0.706683 | − | 0.707530i | \(-0.749809\pi\) | ||||
0.706683 | − | 0.707530i | \(-0.250191\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.221558i | 0.0131240i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.76710 | −0.222365 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.98260 | −0.116624 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.11624i | 0.0654353i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 13.2713i | 0.775316i | 0.921803 | + | 0.387658i | \(0.126716\pi\) | ||||
−0.921803 | + | 0.387658i | \(0.873284\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 15.2009 | 0.885033 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.409212 | −0.0237449 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 17.8480i | 1.03217i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.61268i | 0.208231i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.0359100 | 0.00206298 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 9.45034 | 0.541125 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 14.4325i | 0.823705i | 0.911251 | + | 0.411852i | \(0.135118\pi\) | ||||
−0.911251 | + | 0.411852i | \(0.864882\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.68007i | 0.0955756i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 22.4304 | 1.27191 | 0.635956 | − | 0.771725i | \(-0.280606\pi\) | ||||
0.635956 | + | 0.771725i | \(0.280606\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 24.6010 | 1.39053 | 0.695266 | − | 0.718753i | \(-0.255287\pi\) | ||||
0.695266 | + | 0.718753i | \(0.255287\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − 6.56663i | − 0.369988i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 30.9518i | 1.73842i | 0.494439 | + | 0.869212i | \(0.335374\pi\) | ||||
−0.494439 | + | 0.869212i | \(0.664626\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.0905901 | −0.00507207 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.80203 | −0.100579 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.85656i | 0.214585i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.932345i | 0.0517172i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.03355 | 0.0571557 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 6.68913 | 0.368783 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 33.4297i | − 1.83746i | −0.394884 | − | 0.918731i | \(-0.629215\pi\) | ||||
0.394884 | − | 0.918731i | \(-0.370785\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 6.21251i | 0.340443i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −30.5984 | −1.67177 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 27.1717 | 1.48014 | 0.740069 | − | 0.672530i | \(-0.234793\pi\) | ||||
0.740069 | + | 0.672530i | \(0.234793\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − 0.982459i | − 0.0533599i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.09963i | 0.113701i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.749353 | 0.0403438 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 25.0784i | − 1.34628i | −0.739516 | − | 0.673139i | \(-0.764946\pi\) | ||||
0.739516 | − | 0.673139i | \(-0.235054\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 23.7113i | − 1.26924i | −0.772826 | − | 0.634618i | \(-0.781157\pi\) | ||||
0.772826 | − | 0.634618i | \(-0.218843\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.21934 | 0.171836 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −20.6382 | −1.09846 | −0.549230 | − | 0.835672i | \(-0.685079\pi\) | ||||
−0.549230 | + | 0.835672i | \(0.685079\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 23.3828i | 1.24103i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.392799i | 0.0207891i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −27.2976 | −1.44071 | −0.720355 | − | 0.693605i | \(-0.756021\pi\) | ||||
−0.720355 | + | 0.693605i | \(0.756021\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.0096 | 0.947874 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 1.06893i | − 0.0561042i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 18.9410i | − 0.991419i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 28.7125 | 1.49878 | 0.749390 | − | 0.662128i | \(-0.230347\pi\) | ||||
0.749390 | + | 0.662128i | \(0.230347\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 11.2626 | 0.586307 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 2.93656i | − 0.152459i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 29.1078i | − 1.50715i | −0.657364 | − | 0.753573i | \(-0.728329\pi\) | ||||
0.657364 | − | 0.753573i | \(-0.271671\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.15230 | 0.0595044 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.712688 | 0.0367053 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 19.5975i | 1.00666i | 0.864096 | + | 0.503328i | \(0.167891\pi\) | ||||
−0.864096 | + | 0.503328i | \(0.832109\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 2.05433i | − 0.105247i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 19.5193 | 0.997389 | 0.498694 | − | 0.866778i | \(-0.333813\pi\) | ||||
0.498694 | + | 0.866778i | \(0.333813\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.48040 | −0.0754482 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 10.8009i | − 0.549042i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 10.7701i | − 0.546065i | −0.962005 | − | 0.273033i | \(-0.911973\pi\) | ||||
0.962005 | − | 0.273033i | \(-0.0880267\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 13.0437 | 0.659646 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.81076 | 0.0913405 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 15.6444i | 0.787153i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 29.9845i | − 1.50488i | −0.658661 | − | 0.752440i | \(-0.728877\pi\) | ||||
0.658661 | − | 0.752440i | \(-0.271123\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.100873 | −0.00504998 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 34.4739 | 1.72155 | 0.860773 | − | 0.508989i | \(-0.169981\pi\) | ||||
0.860773 | + | 0.508989i | \(0.169981\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 16.5182i | − 0.822829i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 19.5647i | 0.972179i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.40057 | 0.0694235 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.7405 | 0.728869 | 0.364435 | − | 0.931229i | \(-0.381262\pi\) | ||||
0.364435 | + | 0.931229i | \(0.381262\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.16458i | 0.0574447i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 6.92085i | 0.340553i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −33.3486 | −1.63702 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.0212438 | −0.00104032 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 5.42033i | − 0.264800i | −0.991196 | − | 0.132400i | \(-0.957732\pi\) | ||||
0.991196 | − | 0.132400i | \(-0.0422684\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 9.72201i | − 0.473822i | −0.971531 | − | 0.236911i | \(-0.923865\pi\) | ||||
0.971531 | − | 0.236911i | \(-0.0761350\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −19.9987 | −0.972368 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.681376 | 0.0330516 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.30265i | 0.208220i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − 0.362267i | − 0.0174904i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12.1520 | 0.585341 | 0.292670 | − | 0.956213i | \(-0.405456\pi\) | ||||
0.292670 | + | 0.956213i | \(0.405456\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 30.0836 | 1.44573 | 0.722864 | − | 0.690991i | \(-0.242825\pi\) | ||||
0.722864 | + | 0.690991i | \(0.242825\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − 0.0299225i | − 0.00143467i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.34969i | 0.160238i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.195719 | 0.00934117 | 0.00467058 | − | 0.999989i | \(-0.498513\pi\) | ||||
0.00467058 | + | 0.999989i | \(0.498513\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.98973 | 0.142368 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 28.1256i | 1.33629i | 0.744032 | + | 0.668144i | \(0.232911\pi\) | ||||
−0.744032 | + | 0.668144i | \(0.767089\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 1.88171i | − 0.0892017i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.07337 | 0.0507686 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −12.7288 | −0.600709 | −0.300355 | − | 0.953828i | \(-0.597105\pi\) | ||||
−0.300355 | + | 0.953828i | \(0.597105\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 2.53907i | − 0.119560i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.16383i | 0.0546816i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 11.6466 | 0.546000 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.64289 | −0.170407 | −0.0852035 | − | 0.996364i | \(-0.527154\pi\) | ||||
−0.0852035 | + | 0.996364i | \(0.527154\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 2.35276i | − 0.109817i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 11.4883i | − 0.535064i | −0.963549 | − | 0.267532i | \(-0.913792\pi\) | ||||
0.963549 | − | 0.267532i | \(-0.0862081\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7.98371 | −0.371035 | −0.185517 | − | 0.982641i | \(-0.559396\pi\) | ||||
−0.185517 | + | 0.982641i | \(0.559396\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −0.693521 | −0.0321613 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 27.5689i | 1.27573i | 0.770146 | + | 0.637867i | \(0.220183\pi\) | ||||
−0.770146 | + | 0.637867i | \(0.779817\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 13.9311i | − 0.643280i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.01180 | 0.0466212 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.43499 | −0.111961 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.174982i | 0.00802871i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 8.77951i | 0.401986i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −12.9612 | −0.592210 | −0.296105 | − | 0.955155i | \(-0.595688\pi\) | ||||
−0.296105 | + | 0.955155i | \(0.595688\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −11.0185 | −0.502401 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.341173i | 0.0155239i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 24.1878i | − 1.09831i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8.86309 | −0.401625 | −0.200812 | − | 0.979630i | \(-0.564358\pi\) | ||||
−0.200812 | + | 0.979630i | \(0.564358\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −0.381990 | −0.0172742 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 17.5466i | 0.791865i | 0.918280 | + | 0.395933i | \(0.129579\pi\) | ||||
−0.918280 | + | 0.395933i | \(0.870421\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 0.520847i | − 0.0234578i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4.42599 | 0.198934 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −10.6460 | −0.477536 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 0.153293i | − 0.00686231i | −0.999994 | − | 0.00343116i | \(-0.998908\pi\) | ||||
0.999994 | − | 0.00343116i | \(-0.00109217\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0.857406i | 0.0383061i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −15.5136 | −0.691719 | −0.345860 | − | 0.938286i | \(-0.612413\pi\) | ||||
−0.345860 | + | 0.938286i | \(0.612413\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.778133 | −0.0346264 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.53232i | 0.0680526i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 27.0386i | − 1.19846i | −0.800575 | − | 0.599232i | \(-0.795473\pi\) | ||||
0.800575 | − | 0.599232i | \(-0.204527\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.62368 | 0.381489 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.604204 | 0.0266762 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 36.4053i | − 1.60421i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.50856i | 0.198286i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −0.143475 | −0.00629787 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 15.7310 | 0.689190 | 0.344595 | − | 0.938752i | \(-0.388016\pi\) | ||||
0.344595 | + | 0.938752i | \(0.388016\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 43.4999i | 1.90212i | 0.309009 | + | 0.951059i | \(0.400003\pi\) | ||||
−0.309009 | + | 0.951059i | \(0.599997\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.0178223i | 0 0.000777827i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −12.0718 | −0.525856 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.6707 | −0.507421 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 20.6914i | − 0.897932i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 19.9753i | 0.865227i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 39.0481 | 1.68820 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.74797 | −0.0754303 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 0.674013i | − 0.0290318i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 30.1374i | − 1.29571i | −0.761765 | − | 0.647853i | \(-0.775667\pi\) | ||||
0.761765 | − | 0.647853i | \(-0.224333\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −0.484209 | −0.0207794 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −22.3960 | −0.959341 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 22.1918i | 0.948852i | 0.880295 | + | 0.474426i | \(0.157344\pi\) | ||||
−0.880295 | + | 0.474426i | \(0.842656\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − 12.8637i | − 0.549011i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.133757 | 0.00569823 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.12273 | −0.302889 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.462616i | 0.0196369i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4.64011i | 0.196608i | 0.995156 | + | 0.0983038i | \(0.0313417\pi\) | ||||
−0.995156 | + | 0.0983038i | \(0.968658\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 19.1565 | 0.810235 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.264752 | −0.0111778 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 42.9470i | − 1.81000i | −0.425411 | − | 0.905000i | \(-0.639870\pi\) | ||||
0.425411 | − | 0.905000i | \(-0.360130\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 21.2889i | 0.895629i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −8.90764 | −0.374086 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −28.2672 | −1.18502 | −0.592512 | − | 0.805561i | \(-0.701864\pi\) | ||||
−0.592512 | + | 0.805561i | \(0.701864\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 22.6294i | − 0.947012i | −0.880791 | − | 0.473506i | \(-0.842988\pi\) | ||||
0.880791 | − | 0.473506i | \(-0.157012\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0.902268i | 0.0376928i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.591822 | 0.0246807 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 12.2701 | 0.510809 | 0.255405 | − | 0.966834i | \(-0.417791\pi\) | ||||
0.255405 | + | 0.966834i | \(0.417791\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.21542i | 0.0505113i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 15.1833i | − 0.629909i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.97928 | 0.0819734 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −34.8201 | −1.43963 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 21.0007i | − 0.866793i | −0.901203 | − | 0.433396i | \(-0.857315\pi\) | ||||
0.901203 | − | 0.433396i | \(-0.142685\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 3.10012i | − 0.127738i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.87599 | 0.0771679 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 4.30581 | 0.176819 | 0.0884093 | − | 0.996084i | \(-0.471822\pi\) | ||||
0.0884093 | + | 0.996084i | \(0.471822\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 8.51155i | − 0.348940i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 0.216156i | − 0.00884666i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2.42319 | −0.0990087 | −0.0495044 | − | 0.998774i | \(-0.515764\pi\) | ||||
−0.0495044 | + | 0.998774i | \(0.515764\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6.18973 | −0.252485 | −0.126242 | − | 0.991999i | \(-0.540292\pi\) | ||||
−0.126242 | + | 0.991999i | \(0.540292\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 41.6503i | 1.69613i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 23.1626i | 0.941693i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8.80892 | −0.357543 | −0.178772 | − | 0.983891i | \(-0.557212\pi\) | ||||
−0.178772 | + | 0.983891i | \(0.557212\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.0136234 | 0.000552049 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 35.4696i | − 1.43495i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 19.7718i | − 0.798577i | −0.916825 | − | 0.399289i | \(-0.869257\pi\) | ||||
0.916825 | − | 0.399289i | \(-0.130743\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.838670 | 0.0338185 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −12.9420 | −0.521026 | −0.260513 | − | 0.965470i | \(-0.583892\pi\) | ||||
−0.260513 | + | 0.965470i | \(0.583892\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 17.1723i | − 0.690213i | −0.938563 | − | 0.345107i | \(-0.887843\pi\) | ||||
0.938563 | − | 0.345107i | \(-0.112157\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 2.04354i | − 0.0820042i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0.856726 | 0.0343240 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −24.0899 | −0.963598 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 0.0679899i | − 0.00271526i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 8.05254i | 0.321076i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −13.7312 | −0.546629 | −0.273314 | − | 0.961925i | \(-0.588120\pi\) | ||||
−0.273314 | + | 0.961925i | \(0.588120\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.30331 | 0.0915482 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 44.5153i | 1.76654i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.30258i | 0.210096i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 31.8285 | 1.25912 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −11.7414 | −0.463759 | −0.231879 | − | 0.972745i | \(-0.574487\pi\) | ||||
−0.231879 | + | 0.972745i | \(0.574487\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 2.59560i | − 0.102361i | −0.998689 | − | 0.0511803i | \(-0.983702\pi\) | ||||
0.998689 | − | 0.0511803i | \(-0.0162983\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − 0.804293i | − 0.0316690i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −29.0272 | −1.14118 | −0.570588 | − | 0.821236i | \(-0.693285\pi\) | ||||
−0.570588 | + | 0.821236i | \(0.693285\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.66474 | −0.183107 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − 0.315754i | − 0.0123754i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 39.2320i | 1.53527i | 0.640890 | + | 0.767633i | \(0.278565\pi\) | ||||
−0.640890 | + | 0.767633i | \(0.721435\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −39.2372 | −1.53312 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −25.7824 | −1.00587 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 18.2689i | − 0.711655i | −0.934552 | − | 0.355828i | \(-0.884199\pi\) | ||||
0.934552 | − | 0.355828i | \(-0.115801\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 39.5936i | − 1.54001i | −0.638036 | − | 0.770007i | \(-0.720253\pi\) | ||||
0.638036 | − | 0.770007i | \(-0.279747\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.08285 | 0.0808911 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.18582 | 0.0847625 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 0.452392i | − 0.0175167i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0.111523i | 0.00431173i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.90004 | −0.111955 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8.38015 | −0.323031 | −0.161516 | − | 0.986870i | \(-0.551638\pi\) | ||||
−0.161516 | + | 0.986870i | \(0.551638\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − 0.106750i | − 0.00410883i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 20.5355i | 0.789243i | 0.918844 | + | 0.394621i | \(0.129124\pi\) | ||||
−0.918844 | + | 0.394621i | \(0.870876\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 11.0125 | 0.422620 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.267533 | −0.0102519 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 24.2522i | 0.927983i | 0.885840 | + | 0.463991i | \(0.153583\pi\) | ||||
−0.885840 | + | 0.463991i | \(0.846417\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 25.2353i | − 0.964192i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.94900 | 0.0743592 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −15.5713 | −0.593221 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 30.8579i | 1.17389i | 0.809627 | + | 0.586945i | \(0.199669\pi\) | ||||
−0.809627 | + | 0.586945i | \(0.800331\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.01511i | 0.0765478i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0.460332 | 0.0174614 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 14.5984 | 0.552952 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0.881820i | 0.0333535i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 49.9348i | − 1.88601i | −0.332775 | − | 0.943006i | \(-0.607985\pi\) | ||||
0.332775 | − | 0.943006i | \(-0.392015\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.06794 | −0.0779940 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.48920 | −0.0560867 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 0.354276i | − 0.0133239i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 30.1773i | − 1.13333i | −0.823948 | − | 0.566665i | \(-0.808233\pi\) | ||||
0.823948 | − | 0.566665i | \(-0.191767\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 21.2950 | 0.798625 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −10.4852 | −0.392674 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7.84994i | 0.293571i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0.175206i | 0.00654318i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 25.5563 | 0.953089 | 0.476544 | − | 0.879150i | \(-0.341889\pi\) | ||||
0.476544 | + | 0.879150i | \(0.341889\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 16.5750 | 0.617284 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 1.78885i | − 0.0665279i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 0.0236321i | 0 0.000877674i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −11.4845 | −0.425937 | −0.212969 | − | 0.977059i | \(-0.568313\pi\) | ||||
−0.212969 | + | 0.977059i | \(0.568313\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 26.4468 | 0.979510 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 14.0000i | − 0.517807i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 52.0835i | − 1.92375i | −0.273495 | − | 0.961873i | \(-0.588180\pi\) | ||||
0.273495 | − | 0.961873i | \(-0.411820\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0.222631 | 0.00821185 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 9.38977 | 0.345877 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 25.2269i | − 0.927986i | −0.885839 | − | 0.463993i | \(-0.846416\pi\) | ||||
0.885839 | − | 0.463993i | \(-0.153584\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.534889i | 0.0196496i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −23.8950 | −0.876623 | −0.438311 | − | 0.898823i | \(-0.644423\pi\) | ||||
−0.438311 | + | 0.898823i | \(0.644423\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −23.2588 | −0.852136 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 45.3939i | 1.66087i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 17.7782i | 0.649602i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 29.7013 | 1.08381 | 0.541907 | − | 0.840438i | \(-0.317702\pi\) | ||||
0.541907 | + | 0.840438i | \(0.317702\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.48088 | 0.0539664 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 25.2190i | − 0.917815i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 47.1188i | − 1.71256i | −0.516511 | − | 0.856280i | \(-0.672770\pi\) | ||||
0.516511 | − | 0.856280i | \(-0.327230\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.229955 | −0.00834685 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −11.5153 | −0.417430 | −0.208715 | − | 0.977977i | \(-0.566928\pi\) | ||||
−0.208715 | + | 0.977977i | \(0.566928\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 10.1967i | − 0.369145i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 25.4472i | 0.920046i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 36.6983 | 1.32510 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 27.5195 | 0.992378 | 0.496189 | − | 0.868215i | \(-0.334732\pi\) | ||||
0.496189 | + | 0.868215i | \(0.334732\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.45223i | 0.0883150i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 13.6192i | − 0.489850i | −0.969542 | − | 0.244925i | \(-0.921237\pi\) | ||||
0.969542 | − | 0.244925i | \(-0.0787634\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.547727 | −0.0196749 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.210624 | −0.00755611 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.74895i | 0.134320i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 7.17551i | − 0.256760i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −0.0816005 | −0.00291616 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −21.9246 | −0.782523 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 34.6258i | − 1.23428i | −0.786855 | − | 0.617138i | \(-0.788292\pi\) | ||||
0.786855 | − | 0.617138i | \(-0.211708\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 2.41400i | − 0.0859408i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −9.69262 | −0.344630 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 22.8151 | 0.810189 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.653768i | 0.0231868i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 35.0863i | − 1.24282i | −0.783486 | − | 0.621410i | \(-0.786560\pi\) | ||||
0.783486 | − | 0.621410i | \(-0.213440\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −25.9219 | −0.917051 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.56138 | −0.0905017 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 5.81247i | 0.205118i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 7.39287i | − 0.260565i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0.0308623 | 0.00108641 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 28.3561 | 0.996947 | 0.498473 | − | 0.866905i | \(-0.333894\pi\) | ||||
0.498473 | + | 0.866905i | \(0.333894\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 2.29432i | − 0.0805646i | −0.999188 | − | 0.0402823i | \(-0.987174\pi\) | ||||
0.999188 | − | 0.0402823i | \(-0.0128257\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.74360i | 0.0611508i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 8.27732 | 0.289942 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.59528 | 0.125783 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − 15.8533i | − 0.553958i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 41.7766i | − 1.45801i | −0.684506 | − | 0.729007i | \(-0.739982\pi\) | ||||
0.684506 | − | 0.729007i | \(-0.260018\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −45.2110 | −1.57596 | −0.787979 | − | 0.615702i | \(-0.788872\pi\) | ||||
−0.787979 | + | 0.615702i | \(0.788872\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.0120124 | −0.000418219 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 5.06276i | − 0.176049i | −0.996118 | − | 0.0880246i | \(-0.971945\pi\) | ||||
0.996118 | − | 0.0880246i | \(-0.0280554\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 51.1701i | − 1.77721i | −0.458671 | − | 0.888606i | \(-0.651674\pi\) | ||||
0.458671 | − | 0.888606i | \(-0.348326\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.14369 | −0.0743637 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.87523 | 0.134269 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 18.5791i | − 0.642956i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.89128i | 0.0653721i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 40.5224 | 1.39899 | 0.699495 | − | 0.714638i | \(-0.253408\pi\) | ||||
0.699495 | + | 0.714638i | \(0.253408\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.9819 | 0.999377 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.12485i | 0.0387420i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 33.2037i | − 1.14224i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −10.5457 | −0.362355 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2.41291 | −0.0828109 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.99419i | 0.239758i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 8.02166i | − 0.274656i | −0.990526 | − | 0.137328i | \(-0.956148\pi\) | ||||
0.990526 | − | 0.137328i | \(-0.0438515\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −6.53500 | −0.223492 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0.785744 | 0.0268405 | 0.0134203 | − | 0.999910i | \(-0.495728\pi\) | ||||
0.0134203 | + | 0.999910i | \(0.495728\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 17.1625i | 0.585577i | 0.956177 | + | 0.292789i | \(0.0945833\pi\) | ||||
−0.956177 | + | 0.292789i | \(0.905417\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.381839i | 0.0130130i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 8.01096 | 0.272696 | 0.136348 | − | 0.990661i | \(-0.456463\pi\) | ||||
0.136348 | + | 0.990661i | \(0.456463\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.10896 | 0.105708 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0.200959i | 0.00682494i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 4.80081i | − 0.162856i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −73.8710 | −2.50302 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −32.9243 | −1.11432 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 11.3682i | − 0.384315i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 7.20234i | − 0.243206i | −0.992579 | − | 0.121603i | \(-0.961197\pi\) | ||||
0.992579 | − | 0.121603i | \(-0.0388034\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.34520 | 0.0453724 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 28.3868 | 0.956377 | 0.478188 | − | 0.878257i | \(-0.341294\pi\) | ||||
0.478188 | + | 0.878257i | \(0.341294\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 27.6390i | 0.930126i | 0.885278 | + | 0.465063i | \(0.153968\pi\) | ||||
−0.885278 | + | 0.465063i | \(0.846032\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − 1.54079i | − 0.0517931i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 6.99105 | 0.234737 | 0.117368 | − | 0.993088i | \(-0.462554\pi\) | ||||
0.117368 | + | 0.993088i | \(0.462554\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −20.2674 | −0.679746 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 6.00386i | − 0.201137i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 6.65691i | − 0.222765i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 37.8766 | 1.26607 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.80910 | 0.0604040 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.418685i | 0.0139639i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 11.3798i | 0.379118i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.366187 | 0.0121859 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 10.4923 | 0.348776 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 8.75000i | − 0.290539i | −0.989392 | − | 0.145270i | \(-0.953595\pi\) | ||||
0.989392 | − | 0.145270i | \(-0.0464049\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.05919i | 0.0351311i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −23.5428 | −0.780009 | −0.390005 | − | 0.920813i | \(-0.627527\pi\) | ||||
−0.390005 | + | 0.920813i | \(0.627527\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 10.2337 | 0.338687 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − 0.957901i | − 0.0316672i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 17.8643i | − 0.589932i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 53.5349 | 1.76595 | 0.882976 | − | 0.469417i | \(-0.155536\pi\) | ||||
0.882976 | + | 0.469417i | \(0.155536\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.46290 | 0.0482041 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 56.4510i | 1.85811i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.365363i | 0.0120131i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −49.5546 | −1.62759 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 43.7405 | 1.43508 | 0.717540 | − | 0.696518i | \(-0.245268\pi\) | ||||
0.717540 | + | 0.696518i | \(0.245268\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.995183i | 0.0326158i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 2.27358i | − 0.0744337i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 5.73689 | 0.187617 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 8.90798 | 0.291011 | 0.145506 | − | 0.989357i | \(-0.453519\pi\) | ||||
0.145506 | + | 0.989357i | \(0.453519\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − 2.49360i | − 0.0813755i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 24.1765i | 0.788133i | 0.919082 | + | 0.394066i | \(0.128932\pi\) | ||||
−0.919082 | + | 0.394066i | \(0.871068\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 12.6797 | 0.412907 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.33350 | −0.0433786 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 8.55120i | − 0.277877i | −0.990301 | − | 0.138938i | \(-0.955631\pi\) | ||||
0.990301 | − | 0.138938i | \(-0.0443690\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 45.7277i | − 1.48438i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 3.13732 | 0.101735 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 23.7559 | 0.769529 | 0.384765 | − | 0.923015i | \(-0.374283\pi\) | ||||
0.384765 | + | 0.923015i | \(0.374283\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 19.5512i | − 0.632662i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.00918236i | 0 0.000296823i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 11.4894 | 0.371012 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −21.2960 | −0.686968 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 53.1520i | − 1.71280i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 26.3370i | − 0.847817i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 56.9403 | 1.83108 | 0.915538 | − | 0.402231i | \(-0.131765\pi\) | ||||
0.915538 | + | 0.402231i | \(0.131765\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.390907 | 0.0125578 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 25.9137i | 0.831610i | 0.909454 | + | 0.415805i | \(0.136500\pi\) | ||||
−0.909454 | + | 0.415805i | \(0.863500\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.209585i | 0.00671898i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.0945039 | 0.00302655 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 13.2222 | 0.423014 | 0.211507 | − | 0.977376i | \(-0.432163\pi\) | ||||
0.211507 | + | 0.977376i | \(0.432163\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.577444i | 0.0184552i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 30.4854i | 0.973322i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 39.0935 | 1.24689 | 0.623445 | − | 0.781867i | \(-0.285732\pi\) | ||||
0.623445 | + | 0.781867i | \(0.285732\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −40.6508 | −1.29524 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 0.678020i | − 0.0215816i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 12.1599i | − 0.386664i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −21.0291 | −0.668012 | −0.334006 | − | 0.942571i | \(-0.608401\pi\) | ||||
−0.334006 | + | 0.942571i | \(0.608401\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −3.38849 | −0.107530 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.68387i | 0.148489i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 26.9937i | − 0.854899i | −0.904039 | − | 0.427449i | \(-0.859412\pi\) | ||||
0.904039 | − | 0.427449i | \(-0.140588\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.26158 | 0.0399147 |
(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 | 3584.2.b.i.1793.6 | 12 | ||
4.3 | odd | 2 | 3584.2.b.k.1793.7 | 12 | |||
8.3 | odd | 2 | 3584.2.b.k.1793.6 | 12 | |||
8.5 | even | 2 | inner | 3584.2.b.i.1793.7 | 12 | ||
16.3 | odd | 4 | 3584.2.a.k.1.3 | yes | 6 | ||
16.5 | even | 4 | 3584.2.a.l.1.3 | yes | 6 | ||
16.11 | odd | 4 | 3584.2.a.e.1.4 | ✓ | 6 | ||
16.13 | even | 4 | 3584.2.a.f.1.4 | yes | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3584.2.a.e.1.4 | ✓ | 6 | 16.11 | odd | 4 | ||
3584.2.a.f.1.4 | yes | 6 | 16.13 | even | 4 | ||
3584.2.a.k.1.3 | yes | 6 | 16.3 | odd | 4 | ||
3584.2.a.l.1.3 | yes | 6 | 16.5 | even | 4 | ||
3584.2.b.i.1793.6 | 12 | 1.1 | even | 1 | trivial | ||
3584.2.b.i.1793.7 | 12 | 8.5 | even | 2 | inner | ||
3584.2.b.k.1793.6 | 12 | 8.3 | odd | 2 | |||
3584.2.b.k.1793.7 | 12 | 4.3 | odd | 2 |