Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1890,2,Mod(379,1890)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1890, 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("1890.379");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1890.g (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: | \(15.0917259820\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 379.1 | ||
Root | \(-1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1890.379 |
Dual form | 1890.2.g.i.379.2 |
$q$-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 \(\left(\mathbb{Z}/1890\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(1081\) | \(1541\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.00000i | − | 0.707107i | ||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 1.00000 | − | 2.00000i | 0.447214 | − | 0.894427i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.00000 | − | 1.00000i | −0.632456 | − | 0.316228i | ||||
\(11\) | −1.00000 | −0.301511 | −0.150756 | − | 0.988571i | \(-0.548171\pi\) | ||||
−0.150756 | + | 0.988571i | \(0.548171\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 5.00000i | − | 1.38675i | −0.720577 | − | 0.693375i | \(-0.756123\pi\) | ||
0.720577 | − | 0.693375i | \(-0.243877\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.00000i | 0.970143i | 0.874475 | + | 0.485071i | \(0.161206\pi\) | ||||
−0.874475 | + | 0.485071i | \(0.838794\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.00000 | −1.60591 | −0.802955 | − | 0.596040i | \(-0.796740\pi\) | ||||
−0.802955 | + | 0.596040i | \(0.796740\pi\) | |||||||
\(20\) | −1.00000 | + | 2.00000i | −0.223607 | + | 0.447214i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.00000i | 0.213201i | ||||||||
\(23\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.00000 | − | 4.00000i | −0.600000 | − | 0.800000i | ||||
\(26\) | −5.00000 | −0.980581 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | − | 1.00000i | − | 0.188982i | ||||||
\(29\) | −6.00000 | −1.11417 | −0.557086 | − | 0.830455i | \(-0.688081\pi\) | ||||
−0.557086 | + | 0.830455i | \(0.688081\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.00000 | 0.685994 | ||||||||
\(35\) | 2.00000 | + | 1.00000i | 0.338062 | + | 0.169031i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 4.00000i | − | 0.657596i | −0.944400 | − | 0.328798i | \(-0.893356\pi\) | ||
0.944400 | − | 0.328798i | \(-0.106644\pi\) | |||||||
\(38\) | 7.00000i | 1.13555i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.00000 | + | 1.00000i | 0.316228 | + | 0.158114i | ||||
\(41\) | 3.00000 | 0.468521 | 0.234261 | − | 0.972174i | \(-0.424733\pi\) | ||||
0.234261 | + | 0.972174i | \(0.424733\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 11.0000i | − | 1.67748i | −0.544529 | − | 0.838742i | \(-0.683292\pi\) | ||
0.544529 | − | 0.838742i | \(-0.316708\pi\) | |||||||
\(44\) | 1.00000 | 0.150756 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 1.00000i | − | 0.145865i | −0.997337 | − | 0.0729325i | \(-0.976764\pi\) | ||
0.997337 | − | 0.0729325i | \(-0.0232358\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | −4.00000 | + | 3.00000i | −0.565685 | + | 0.424264i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 5.00000i | 0.693375i | ||||||||
\(53\) | 1.00000i | 0.137361i | 0.997639 | + | 0.0686803i | \(0.0218788\pi\) | ||||
−0.997639 | + | 0.0686803i | \(0.978121\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.00000 | + | 2.00000i | −0.134840 | + | 0.269680i | ||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 6.00000i | 0.787839i | ||||||||
\(59\) | −2.00000 | −0.260378 | −0.130189 | − | 0.991489i | \(-0.541558\pi\) | ||||
−0.130189 | + | 0.991489i | \(0.541558\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.00000 | −0.256074 | −0.128037 | − | 0.991769i | \(-0.540868\pi\) | ||||
−0.128037 | + | 0.991769i | \(0.540868\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −10.0000 | − | 5.00000i | −1.24035 | − | 0.620174i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 15.0000i | 1.83254i | 0.400559 | + | 0.916271i | \(0.368816\pi\) | ||||
−0.400559 | + | 0.916271i | \(0.631184\pi\) | |||||||
\(68\) | − | 4.00000i | − | 0.485071i | ||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.00000 | − | 2.00000i | 0.119523 | − | 0.239046i | ||||
\(71\) | −16.0000 | −1.89885 | −0.949425 | − | 0.313993i | \(-0.898333\pi\) | ||||
−0.949425 | + | 0.313993i | \(0.898333\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 11.0000i | − | 1.28745i | −0.765256 | − | 0.643726i | \(-0.777388\pi\) | ||
0.765256 | − | 0.643726i | \(-0.222612\pi\) | |||||||
\(74\) | −4.00000 | −0.464991 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 7.00000 | 0.802955 | ||||||||
\(77\) | − | 1.00000i | − | 0.113961i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10.0000 | −1.12509 | −0.562544 | − | 0.826767i | \(-0.690177\pi\) | ||||
−0.562544 | + | 0.826767i | \(0.690177\pi\) | |||||||
\(80\) | 1.00000 | − | 2.00000i | 0.111803 | − | 0.223607i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − | 3.00000i | − | 0.331295i | ||||||
\(83\) | 7.00000i | 0.768350i | 0.923260 | + | 0.384175i | \(0.125514\pi\) | ||||
−0.923260 | + | 0.384175i | \(0.874486\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.00000 | + | 4.00000i | 0.867722 | + | 0.433861i | ||||
\(86\) | −11.0000 | −1.18616 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − | 1.00000i | − | 0.106600i | ||||||
\(89\) | 1.00000 | 0.106000 | 0.0529999 | − | 0.998595i | \(-0.483122\pi\) | ||||
0.0529999 | + | 0.998595i | \(0.483122\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.00000 | 0.524142 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.00000 | −0.103142 | ||||||||
\(95\) | −7.00000 | + | 14.0000i | −0.718185 | + | 1.43637i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 14.0000i | − | 1.42148i | −0.703452 | − | 0.710742i | \(-0.748359\pi\) | ||
0.703452 | − | 0.710742i | \(-0.251641\pi\) | |||||||
\(98\) | 1.00000i | 0.101015i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 3.00000 | + | 4.00000i | 0.300000 | + | 0.400000i | ||||
\(101\) | −5.00000 | −0.497519 | −0.248759 | − | 0.968565i | \(-0.580023\pi\) | ||||
−0.248759 | + | 0.968565i | \(0.580023\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.00000i | 0.591198i | 0.955312 | + | 0.295599i | \(0.0955191\pi\) | ||||
−0.955312 | + | 0.295599i | \(0.904481\pi\) | |||||||
\(104\) | 5.00000 | 0.490290 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.00000 | 0.0971286 | ||||||||
\(107\) | 6.00000i | 0.580042i | 0.957020 | + | 0.290021i | \(0.0936623\pi\) | ||||
−0.957020 | + | 0.290021i | \(0.906338\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 15.0000 | 1.43674 | 0.718370 | − | 0.695662i | \(-0.244889\pi\) | ||||
0.718370 | + | 0.695662i | \(0.244889\pi\) | |||||||
\(110\) | 2.00000 | + | 1.00000i | 0.190693 | + | 0.0953463i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.00000i | 0.0944911i | ||||||||
\(113\) | − | 15.0000i | − | 1.41108i | −0.708669 | − | 0.705541i | \(-0.750704\pi\) | ||
0.708669 | − | 0.705541i | \(-0.249296\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 6.00000 | 0.557086 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2.00000i | 0.184115i | ||||||||
\(119\) | −4.00000 | −0.366679 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.0000 | −0.909091 | ||||||||
\(122\) | 2.00000i | 0.181071i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.0000 | + | 2.00000i | −0.983870 | + | 0.178885i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 9.00000i | − | 0.798621i | −0.916816 | − | 0.399310i | \(-0.869250\pi\) | ||
0.916816 | − | 0.399310i | \(-0.130750\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −5.00000 | + | 10.0000i | −0.438529 | + | 0.877058i | ||||
\(131\) | −4.00000 | −0.349482 | −0.174741 | − | 0.984614i | \(-0.555909\pi\) | ||||
−0.174741 | + | 0.984614i | \(0.555909\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 7.00000i | − | 0.606977i | ||||||
\(134\) | 15.0000 | 1.29580 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.00000 | −0.342997 | ||||||||
\(137\) | 17.0000i | 1.45241i | 0.687479 | + | 0.726204i | \(0.258717\pi\) | ||||
−0.687479 | + | 0.726204i | \(0.741283\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 20.0000 | 1.69638 | 0.848189 | − | 0.529694i | \(-0.177693\pi\) | ||||
0.848189 | + | 0.529694i | \(0.177693\pi\) | |||||||
\(140\) | −2.00000 | − | 1.00000i | −0.169031 | − | 0.0845154i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 16.0000i | 1.34269i | ||||||||
\(143\) | 5.00000i | 0.418121i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.00000 | + | 12.0000i | −0.498273 | + | 0.996546i | ||||
\(146\) | −11.0000 | −0.910366 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4.00000i | 0.328798i | ||||||||
\(149\) | 12.0000 | 0.983078 | 0.491539 | − | 0.870855i | \(-0.336434\pi\) | ||||
0.491539 | + | 0.870855i | \(0.336434\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −10.0000 | −0.813788 | −0.406894 | − | 0.913475i | \(-0.633388\pi\) | ||||
−0.406894 | + | 0.913475i | \(0.633388\pi\) | |||||||
\(152\) | − | 7.00000i | − | 0.567775i | ||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1.00000 | −0.0805823 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.0000i | 1.11732i | 0.829396 | + | 0.558661i | \(0.188685\pi\) | ||||
−0.829396 | + | 0.558661i | \(0.811315\pi\) | |||||||
\(158\) | 10.0000i | 0.795557i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2.00000 | − | 1.00000i | −0.158114 | − | 0.0790569i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 12.0000i | − | 0.939913i | −0.882690 | − | 0.469956i | \(-0.844270\pi\) | ||
0.882690 | − | 0.469956i | \(-0.155730\pi\) | |||||||
\(164\) | −3.00000 | −0.234261 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 7.00000 | 0.543305 | ||||||||
\(167\) | 20.0000i | 1.54765i | 0.633402 | + | 0.773823i | \(0.281658\pi\) | ||||
−0.633402 | + | 0.773823i | \(0.718342\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.0000 | −0.923077 | ||||||||
\(170\) | 4.00000 | − | 8.00000i | 0.306786 | − | 0.613572i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 11.0000i | 0.838742i | ||||||||
\(173\) | 14.0000i | 1.06440i | 0.846619 | + | 0.532200i | \(0.178635\pi\) | ||||
−0.846619 | + | 0.532200i | \(0.821365\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.00000 | − | 3.00000i | 0.302372 | − | 0.226779i | ||||
\(176\) | −1.00000 | −0.0753778 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − | 1.00000i | − | 0.0749532i | ||||||
\(179\) | 7.00000 | 0.523205 | 0.261602 | − | 0.965176i | \(-0.415749\pi\) | ||||
0.261602 | + | 0.965176i | \(0.415749\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.0000 | −1.04061 | −0.520306 | − | 0.853980i | \(-0.674182\pi\) | ||||
−0.520306 | + | 0.853980i | \(0.674182\pi\) | |||||||
\(182\) | − | 5.00000i | − | 0.370625i | ||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −8.00000 | − | 4.00000i | −0.588172 | − | 0.294086i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 4.00000i | − | 0.292509i | ||||||
\(188\) | 1.00000i | 0.0729325i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 14.0000 | + | 7.00000i | 1.01567 | + | 0.507833i | ||||
\(191\) | −11.0000 | −0.795932 | −0.397966 | − | 0.917400i | \(-0.630284\pi\) | ||||
−0.397966 | + | 0.917400i | \(0.630284\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 18.0000i | − | 1.29567i | −0.761781 | − | 0.647834i | \(-0.775675\pi\) | ||
0.761781 | − | 0.647834i | \(-0.224325\pi\) | |||||||
\(194\) | −14.0000 | −1.00514 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | − | 15.0000i | − | 1.06871i | −0.845262 | − | 0.534353i | \(-0.820555\pi\) | ||
0.845262 | − | 0.534353i | \(-0.179445\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.00000 | −0.496217 | −0.248108 | − | 0.968732i | \(-0.579809\pi\) | ||||
−0.248108 | + | 0.968732i | \(0.579809\pi\) | |||||||
\(200\) | 4.00000 | − | 3.00000i | 0.282843 | − | 0.212132i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 5.00000i | 0.351799i | ||||||||
\(203\) | − | 6.00000i | − | 0.421117i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.00000 | − | 6.00000i | 0.209529 | − | 0.419058i | ||||
\(206\) | 6.00000 | 0.418040 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − | 5.00000i | − | 0.346688i | ||||||
\(209\) | 7.00000 | 0.484200 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.0000 | 0.688428 | 0.344214 | − | 0.938891i | \(-0.388145\pi\) | ||||
0.344214 | + | 0.938891i | \(0.388145\pi\) | |||||||
\(212\) | − | 1.00000i | − | 0.0686803i | ||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 6.00000 | 0.410152 | ||||||||
\(215\) | −22.0000 | − | 11.0000i | −1.50039 | − | 0.750194i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | − | 15.0000i | − | 1.01593i | ||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1.00000 | − | 2.00000i | 0.0674200 | − | 0.134840i | ||||
\(221\) | 20.0000 | 1.34535 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 14.0000i | − | 0.937509i | −0.883328 | − | 0.468755i | \(-0.844703\pi\) | ||
0.883328 | − | 0.468755i | \(-0.155297\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −15.0000 | −0.997785 | ||||||||
\(227\) | − | 7.00000i | − | 0.464606i | −0.972643 | − | 0.232303i | \(-0.925374\pi\) | ||
0.972643 | − | 0.232303i | \(-0.0746261\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −14.0000 | −0.925146 | −0.462573 | − | 0.886581i | \(-0.653074\pi\) | ||||
−0.462573 | + | 0.886581i | \(0.653074\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − | 6.00000i | − | 0.393919i | ||||||
\(233\) | − | 3.00000i | − | 0.196537i | −0.995160 | − | 0.0982683i | \(-0.968670\pi\) | ||
0.995160 | − | 0.0982683i | \(-0.0313303\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.00000 | − | 1.00000i | −0.130466 | − | 0.0652328i | ||||
\(236\) | 2.00000 | 0.130189 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 4.00000i | 0.259281i | ||||||||
\(239\) | −4.00000 | −0.258738 | −0.129369 | − | 0.991596i | \(-0.541295\pi\) | ||||
−0.129369 | + | 0.991596i | \(0.541295\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.0000 | −0.644157 | −0.322078 | − | 0.946713i | \(-0.604381\pi\) | ||||
−0.322078 | + | 0.946713i | \(0.604381\pi\) | |||||||
\(242\) | 10.0000i | 0.642824i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2.00000 | 0.128037 | ||||||||
\(245\) | −1.00000 | + | 2.00000i | −0.0638877 | + | 0.127775i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 35.0000i | 2.22700i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 2.00000 | + | 11.0000i | 0.126491 | + | 0.695701i | ||||
\(251\) | 24.0000 | 1.51487 | 0.757433 | − | 0.652913i | \(-0.226453\pi\) | ||||
0.757433 | + | 0.652913i | \(0.226453\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −9.00000 | −0.564710 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − | 28.0000i | − | 1.74659i | −0.487190 | − | 0.873296i | \(-0.661978\pi\) | ||
0.487190 | − | 0.873296i | \(-0.338022\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.00000 | 0.248548 | ||||||||
\(260\) | 10.0000 | + | 5.00000i | 0.620174 | + | 0.310087i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 4.00000i | 0.247121i | ||||||||
\(263\) | − | 12.0000i | − | 0.739952i | −0.929041 | − | 0.369976i | \(-0.879366\pi\) | ||
0.929041 | − | 0.369976i | \(-0.120634\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.00000 | + | 1.00000i | 0.122859 | + | 0.0614295i | ||||
\(266\) | −7.00000 | −0.429198 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − | 15.0000i | − | 0.916271i | ||||||
\(269\) | 26.0000 | 1.58525 | 0.792624 | − | 0.609711i | \(-0.208714\pi\) | ||||
0.792624 | + | 0.609711i | \(0.208714\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.00000 | 0.303728 | 0.151864 | − | 0.988401i | \(-0.451472\pi\) | ||||
0.151864 | + | 0.988401i | \(0.451472\pi\) | |||||||
\(272\) | 4.00000i | 0.242536i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 17.0000 | 1.02701 | ||||||||
\(275\) | 3.00000 | + | 4.00000i | 0.180907 | + | 0.241209i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 8.00000i | − | 0.480673i | −0.970690 | − | 0.240337i | \(-0.922742\pi\) | ||
0.970690 | − | 0.240337i | \(-0.0772579\pi\) | |||||||
\(278\) | − | 20.0000i | − | 1.19952i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1.00000 | + | 2.00000i | −0.0597614 | + | 0.119523i | ||||
\(281\) | 14.0000 | 0.835170 | 0.417585 | − | 0.908638i | \(-0.362877\pi\) | ||||
0.417585 | + | 0.908638i | \(0.362877\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 4.00000i | − | 0.237775i | −0.992908 | − | 0.118888i | \(-0.962067\pi\) | ||
0.992908 | − | 0.118888i | \(-0.0379328\pi\) | |||||||
\(284\) | 16.0000 | 0.949425 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 5.00000 | 0.295656 | ||||||||
\(287\) | 3.00000i | 0.177084i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 12.0000 | + | 6.00000i | 0.704664 | + | 0.352332i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 11.0000i | 0.643726i | ||||||||
\(293\) | 26.0000i | 1.51894i | 0.650545 | + | 0.759468i | \(0.274541\pi\) | ||||
−0.650545 | + | 0.759468i | \(0.725459\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.00000 | + | 4.00000i | −0.116445 | + | 0.232889i | ||||
\(296\) | 4.00000 | 0.232495 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − | 12.0000i | − | 0.695141i | ||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 11.0000 | 0.634029 | ||||||||
\(302\) | 10.0000i | 0.575435i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −7.00000 | −0.401478 | ||||||||
\(305\) | −2.00000 | + | 4.00000i | −0.114520 | + | 0.229039i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 22.0000i | 1.25561i | 0.778372 | + | 0.627803i | \(0.216046\pi\) | ||||
−0.778372 | + | 0.627803i | \(0.783954\pi\) | |||||||
\(308\) | 1.00000i | 0.0569803i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 14.0000 | 0.793867 | 0.396934 | − | 0.917847i | \(-0.370074\pi\) | ||||
0.396934 | + | 0.917847i | \(0.370074\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 13.0000i | − | 0.734803i | −0.930062 | − | 0.367402i | \(-0.880247\pi\) | ||
0.930062 | − | 0.367402i | \(-0.119753\pi\) | |||||||
\(314\) | 14.0000 | 0.790066 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 10.0000 | 0.562544 | ||||||||
\(317\) | − | 25.0000i | − | 1.40414i | −0.712108 | − | 0.702070i | \(-0.752259\pi\) | ||
0.712108 | − | 0.702070i | \(-0.247741\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.00000 | 0.335936 | ||||||||
\(320\) | −1.00000 | + | 2.00000i | −0.0559017 | + | 0.111803i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 28.0000i | − | 1.55796i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −20.0000 | + | 15.0000i | −1.10940 | + | 0.832050i | ||||
\(326\) | −12.0000 | −0.664619 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 3.00000i | 0.165647i | ||||||||
\(329\) | 1.00000 | 0.0551318 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.0000 | 0.659580 | 0.329790 | − | 0.944054i | \(-0.393022\pi\) | ||||
0.329790 | + | 0.944054i | \(0.393022\pi\) | |||||||
\(332\) | − | 7.00000i | − | 0.384175i | ||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 20.0000 | 1.09435 | ||||||||
\(335\) | 30.0000 | + | 15.0000i | 1.63908 | + | 0.819538i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.00000i | 0.108947i | 0.998515 | + | 0.0544735i | \(0.0173480\pi\) | ||||
−0.998515 | + | 0.0544735i | \(0.982652\pi\) | |||||||
\(338\) | 12.0000i | 0.652714i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −8.00000 | − | 4.00000i | −0.433861 | − | 0.216930i | ||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 1.00000i | − | 0.0539949i | ||||||
\(344\) | 11.0000 | 0.593080 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 14.0000 | 0.752645 | ||||||||
\(347\) | − | 28.0000i | − | 1.50312i | −0.659665 | − | 0.751559i | \(-0.729302\pi\) | ||
0.659665 | − | 0.751559i | \(-0.270698\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(350\) | −3.00000 | − | 4.00000i | −0.160357 | − | 0.213809i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.00000i | 0.0533002i | ||||||||
\(353\) | 6.00000i | 0.319348i | 0.987170 | + | 0.159674i | \(0.0510443\pi\) | ||||
−0.987170 | + | 0.159674i | \(0.948956\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −16.0000 | + | 32.0000i | −0.849192 | + | 1.69838i | ||||
\(356\) | −1.00000 | −0.0529999 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − | 7.00000i | − | 0.369961i | ||||||
\(359\) | 5.00000 | 0.263890 | 0.131945 | − | 0.991257i | \(-0.457878\pi\) | ||||
0.131945 | + | 0.991257i | \(0.457878\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 30.0000 | 1.57895 | ||||||||
\(362\) | 14.0000i | 0.735824i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −5.00000 | −0.262071 | ||||||||
\(365\) | −22.0000 | − | 11.0000i | −1.15153 | − | 0.575766i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 2.00000i | − | 0.104399i | −0.998637 | − | 0.0521996i | \(-0.983377\pi\) | ||
0.998637 | − | 0.0521996i | \(-0.0166232\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −4.00000 | + | 8.00000i | −0.207950 | + | 0.415900i | ||||
\(371\) | −1.00000 | −0.0519174 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 18.0000i | − | 0.932005i | −0.884783 | − | 0.466002i | \(-0.845694\pi\) | ||
0.884783 | − | 0.466002i | \(-0.154306\pi\) | |||||||
\(374\) | −4.00000 | −0.206835 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.00000 | 0.0515711 | ||||||||
\(377\) | 30.0000i | 1.54508i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10.0000 | 0.513665 | 0.256833 | − | 0.966456i | \(-0.417321\pi\) | ||||
0.256833 | + | 0.966456i | \(0.417321\pi\) | |||||||
\(380\) | 7.00000 | − | 14.0000i | 0.359092 | − | 0.718185i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 11.0000i | 0.562809i | ||||||||
\(383\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.00000 | − | 1.00000i | −0.101929 | − | 0.0509647i | ||||
\(386\) | −18.0000 | −0.916176 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 14.0000i | 0.710742i | ||||||||
\(389\) | −6.00000 | −0.304212 | −0.152106 | − | 0.988364i | \(-0.548606\pi\) | ||||
−0.152106 | + | 0.988364i | \(0.548606\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | − | 1.00000i | − | 0.0505076i | ||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −15.0000 | −0.755689 | ||||||||
\(395\) | −10.0000 | + | 20.0000i | −0.503155 | + | 1.00631i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 34.0000i | − | 1.70641i | −0.521575 | − | 0.853206i | \(-0.674655\pi\) | ||
0.521575 | − | 0.853206i | \(-0.325345\pi\) | |||||||
\(398\) | 7.00000i | 0.350878i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.00000 | − | 4.00000i | −0.150000 | − | 0.200000i | ||||
\(401\) | 30.0000 | 1.49813 | 0.749064 | − | 0.662497i | \(-0.230503\pi\) | ||||
0.749064 | + | 0.662497i | \(0.230503\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 5.00000 | 0.248759 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −6.00000 | −0.297775 | ||||||||
\(407\) | 4.00000i | 0.198273i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −22.0000 | −1.08783 | −0.543915 | − | 0.839140i | \(-0.683059\pi\) | ||||
−0.543915 | + | 0.839140i | \(0.683059\pi\) | |||||||
\(410\) | −6.00000 | − | 3.00000i | −0.296319 | − | 0.148159i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 6.00000i | − | 0.295599i | ||||||
\(413\) | − | 2.00000i | − | 0.0984136i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 14.0000 | + | 7.00000i | 0.687233 | + | 0.343616i | ||||
\(416\) | −5.00000 | −0.245145 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − | 7.00000i | − | 0.342381i | ||||||
\(419\) | 18.0000 | 0.879358 | 0.439679 | − | 0.898155i | \(-0.355092\pi\) | ||||
0.439679 | + | 0.898155i | \(0.355092\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11.0000 | −0.536107 | −0.268054 | − | 0.963404i | \(-0.586380\pi\) | ||||
−0.268054 | + | 0.963404i | \(0.586380\pi\) | |||||||
\(422\) | − | 10.0000i | − | 0.486792i | ||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.00000 | −0.0485643 | ||||||||
\(425\) | 16.0000 | − | 12.0000i | 0.776114 | − | 0.582086i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 2.00000i | − | 0.0967868i | ||||||
\(428\) | − | 6.00000i | − | 0.290021i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −11.0000 | + | 22.0000i | −0.530467 | + | 1.06093i | ||||
\(431\) | −3.00000 | −0.144505 | −0.0722525 | − | 0.997386i | \(-0.523019\pi\) | ||||
−0.0722525 | + | 0.997386i | \(0.523019\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 17.0000i | − | 0.816968i | −0.912766 | − | 0.408484i | \(-0.866058\pi\) | ||
0.912766 | − | 0.408484i | \(-0.133942\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −15.0000 | −0.718370 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.00000 | 0.143182 | 0.0715911 | − | 0.997434i | \(-0.477192\pi\) | ||||
0.0715911 | + | 0.997434i | \(0.477192\pi\) | |||||||
\(440\) | −2.00000 | − | 1.00000i | −0.0953463 | − | 0.0476731i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 20.0000i | − | 0.951303i | ||||||
\(443\) | − | 36.0000i | − | 1.71041i | −0.518289 | − | 0.855206i | \(-0.673431\pi\) | ||
0.518289 | − | 0.855206i | \(-0.326569\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.00000 | − | 2.00000i | 0.0474045 | − | 0.0948091i | ||||
\(446\) | −14.0000 | −0.662919 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | − | 1.00000i | − | 0.0472456i | ||||||
\(449\) | −18.0000 | −0.849473 | −0.424736 | − | 0.905317i | \(-0.639633\pi\) | ||||
−0.424736 | + | 0.905317i | \(0.639633\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.00000 | −0.141264 | ||||||||
\(452\) | 15.0000i | 0.705541i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −7.00000 | −0.328526 | ||||||||
\(455\) | 5.00000 | − | 10.0000i | 0.234404 | − | 0.468807i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 22.0000i | − | 1.02912i | −0.857455 | − | 0.514558i | \(-0.827956\pi\) | ||
0.857455 | − | 0.514558i | \(-0.172044\pi\) | |||||||
\(458\) | 14.0000i | 0.654177i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 15.0000 | 0.698620 | 0.349310 | − | 0.937007i | \(-0.386416\pi\) | ||||
0.349310 | + | 0.937007i | \(0.386416\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 21.0000i | − | 0.975953i | −0.872857 | − | 0.487976i | \(-0.837735\pi\) | ||
0.872857 | − | 0.487976i | \(-0.162265\pi\) | |||||||
\(464\) | −6.00000 | −0.278543 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3.00000 | −0.138972 | ||||||||
\(467\) | − | 28.0000i | − | 1.29569i | −0.761774 | − | 0.647843i | \(-0.775671\pi\) | ||
0.761774 | − | 0.647843i | \(-0.224329\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −15.0000 | −0.692636 | ||||||||
\(470\) | −1.00000 | + | 2.00000i | −0.0461266 | + | 0.0922531i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − | 2.00000i | − | 0.0920575i | ||||||
\(473\) | 11.0000i | 0.505781i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 21.0000 | + | 28.0000i | 0.963546 | + | 1.28473i | ||||
\(476\) | 4.00000 | 0.183340 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 4.00000i | 0.182956i | ||||||||
\(479\) | 14.0000 | 0.639676 | 0.319838 | − | 0.947472i | \(-0.396371\pi\) | ||||
0.319838 | + | 0.947472i | \(0.396371\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −20.0000 | −0.911922 | ||||||||
\(482\) | 10.0000i | 0.455488i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 10.0000 | 0.454545 | ||||||||
\(485\) | −28.0000 | − | 14.0000i | −1.27141 | − | 0.635707i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 33.0000i | − | 1.49537i | −0.664052 | − | 0.747686i | \(-0.731165\pi\) | ||
0.664052 | − | 0.747686i | \(-0.268835\pi\) | |||||||
\(488\) | − | 2.00000i | − | 0.0905357i | ||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 2.00000 | + | 1.00000i | 0.0903508 | + | 0.0451754i | ||||
\(491\) | 36.0000 | 1.62466 | 0.812329 | − | 0.583200i | \(-0.198200\pi\) | ||||
0.812329 | + | 0.583200i | \(0.198200\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 24.0000i | − | 1.08091i | ||||||
\(494\) | 35.0000 | 1.57472 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 16.0000i | − | 0.717698i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 40.0000 | 1.79065 | 0.895323 | − | 0.445418i | \(-0.146945\pi\) | ||||
0.895323 | + | 0.445418i | \(0.146945\pi\) | |||||||
\(500\) | 11.0000 | − | 2.00000i | 0.491935 | − | 0.0894427i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 24.0000i | − | 1.07117i | ||||||
\(503\) | 39.0000i | 1.73892i | 0.494000 | + | 0.869462i | \(0.335534\pi\) | ||||
−0.494000 | + | 0.869462i | \(0.664466\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.00000 | + | 10.0000i | −0.222497 | + | 0.444994i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 9.00000i | 0.399310i | ||||||||
\(509\) | 38.0000 | 1.68432 | 0.842160 | − | 0.539227i | \(-0.181284\pi\) | ||||
0.842160 | + | 0.539227i | \(0.181284\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 11.0000 | 0.486611 | ||||||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −28.0000 | −1.23503 | ||||||||
\(515\) | 12.0000 | + | 6.00000i | 0.528783 | + | 0.264392i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.00000i | 0.0439799i | ||||||||
\(518\) | − | 4.00000i | − | 0.175750i | ||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 5.00000 | − | 10.0000i | 0.219265 | − | 0.438529i | ||||
\(521\) | −33.0000 | −1.44576 | −0.722878 | − | 0.690976i | \(-0.757181\pi\) | ||||
−0.722878 | + | 0.690976i | \(0.757181\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 12.0000i | 0.524723i | 0.964970 | + | 0.262362i | \(0.0845013\pi\) | ||||
−0.964970 | + | 0.262362i | \(0.915499\pi\) | |||||||
\(524\) | 4.00000 | 0.174741 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −12.0000 | −0.523225 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 23.0000 | 1.00000 | ||||||||
\(530\) | 1.00000 | − | 2.00000i | 0.0434372 | − | 0.0868744i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 7.00000i | 0.303488i | ||||||||
\(533\) | − | 15.0000i | − | 0.649722i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 12.0000 | + | 6.00000i | 0.518805 | + | 0.259403i | ||||
\(536\) | −15.0000 | −0.647901 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 26.0000i | − | 1.12094i | ||||||
\(539\) | 1.00000 | 0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17.0000 | −0.730887 | −0.365444 | − | 0.930834i | \(-0.619083\pi\) | ||||
−0.365444 | + | 0.930834i | \(0.619083\pi\) | |||||||
\(542\) | − | 5.00000i | − | 0.214768i | ||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 4.00000 | 0.171499 | ||||||||
\(545\) | 15.0000 | − | 30.0000i | 0.642529 | − | 1.28506i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 32.0000i | 1.36822i | 0.729378 | + | 0.684111i | \(0.239809\pi\) | ||||
−0.729378 | + | 0.684111i | \(0.760191\pi\) | |||||||
\(548\) | − | 17.0000i | − | 0.726204i | ||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 4.00000 | − | 3.00000i | 0.170561 | − | 0.127920i | ||||
\(551\) | 42.0000 | 1.78926 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 10.0000i | − | 0.425243i | ||||||
\(554\) | −8.00000 | −0.339887 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −20.0000 | −0.848189 | ||||||||
\(557\) | 30.0000i | 1.27114i | 0.772043 | + | 0.635570i | \(0.219235\pi\) | ||||
−0.772043 | + | 0.635570i | \(0.780765\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −55.0000 | −2.32625 | ||||||||
\(560\) | 2.00000 | + | 1.00000i | 0.0845154 | + | 0.0422577i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | − | 14.0000i | − | 0.590554i | ||||||
\(563\) | − | 21.0000i | − | 0.885044i | −0.896758 | − | 0.442522i | \(-0.854084\pi\) | ||
0.896758 | − | 0.442522i | \(-0.145916\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −30.0000 | − | 15.0000i | −1.26211 | − | 0.631055i | ||||
\(566\) | −4.00000 | −0.168133 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 16.0000i | − | 0.671345i | ||||||
\(569\) | −42.0000 | −1.76073 | −0.880366 | − | 0.474295i | \(-0.842703\pi\) | ||||
−0.880366 | + | 0.474295i | \(0.842703\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10.0000 | 0.418487 | 0.209243 | − | 0.977864i | \(-0.432900\pi\) | ||||
0.209243 | + | 0.977864i | \(0.432900\pi\) | |||||||
\(572\) | − | 5.00000i | − | 0.209061i | ||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 3.00000 | 0.125218 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9.00000i | 0.374675i | 0.982296 | + | 0.187337i | \(0.0599858\pi\) | ||||
−0.982296 | + | 0.187337i | \(0.940014\pi\) | |||||||
\(578\) | − | 1.00000i | − | 0.0415945i | ||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 6.00000 | − | 12.0000i | 0.249136 | − | 0.498273i | ||||
\(581\) | −7.00000 | −0.290409 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 1.00000i | − | 0.0414158i | ||||||
\(584\) | 11.0000 | 0.455183 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 26.0000 | 1.07405 | ||||||||
\(587\) | − | 4.00000i | − | 0.165098i | −0.996587 | − | 0.0825488i | \(-0.973694\pi\) | ||
0.996587 | − | 0.0825488i | \(-0.0263060\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 4.00000 | + | 2.00000i | 0.164677 | + | 0.0823387i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − | 4.00000i | − | 0.164399i | ||||||
\(593\) | 34.0000i | 1.39621i | 0.715994 | + | 0.698106i | \(0.245974\pi\) | ||||
−0.715994 | + | 0.698106i | \(0.754026\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.00000 | + | 8.00000i | −0.163984 | + | 0.327968i | ||||
\(596\) | −12.0000 | −0.491539 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −19.0000 | −0.776319 | −0.388159 | − | 0.921592i | \(-0.626889\pi\) | ||||
−0.388159 | + | 0.921592i | \(0.626889\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12.0000 | −0.489490 | −0.244745 | − | 0.969587i | \(-0.578704\pi\) | ||||
−0.244745 | + | 0.969587i | \(0.578704\pi\) | |||||||
\(602\) | − | 11.0000i | − | 0.448327i | ||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 10.0000 | 0.406894 | ||||||||
\(605\) | −10.0000 | + | 20.0000i | −0.406558 | + | 0.813116i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 20.0000i | 0.811775i | 0.913923 | + | 0.405887i | \(0.133038\pi\) | ||||
−0.913923 | + | 0.405887i | \(0.866962\pi\) | |||||||
\(608\) | 7.00000i | 0.283887i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 4.00000 | + | 2.00000i | 0.161955 | + | 0.0809776i | ||||
\(611\) | −5.00000 | −0.202278 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 44.0000i | − | 1.77714i | −0.458738 | − | 0.888572i | \(-0.651698\pi\) | ||
0.458738 | − | 0.888572i | \(-0.348302\pi\) | |||||||
\(614\) | 22.0000 | 0.887848 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.00000 | 0.0402911 | ||||||||
\(617\) | 6.00000i | 0.241551i | 0.992680 | + | 0.120775i | \(0.0385381\pi\) | ||||
−0.992680 | + | 0.120775i | \(0.961462\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −33.0000 | −1.32638 | −0.663191 | − | 0.748450i | \(-0.730798\pi\) | ||||
−0.663191 | + | 0.748450i | \(0.730798\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 14.0000i | − | 0.561349i | ||||||
\(623\) | 1.00000i | 0.0400642i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7.00000 | + | 24.0000i | −0.280000 | + | 0.960000i | ||||
\(626\) | −13.0000 | −0.519584 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 14.0000i | − | 0.558661i | ||||||
\(629\) | 16.0000 | 0.637962 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −18.0000 | −0.716569 | −0.358284 | − | 0.933613i | \(-0.616638\pi\) | ||||
−0.358284 | + | 0.933613i | \(0.616638\pi\) | |||||||
\(632\) | − | 10.0000i | − | 0.397779i | ||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −25.0000 | −0.992877 | ||||||||
\(635\) | −18.0000 | − | 9.00000i | −0.714308 | − | 0.357154i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.00000i | 0.198107i | ||||||||
\(638\) | − | 6.00000i | − | 0.237542i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 2.00000 | + | 1.00000i | 0.0790569 | + | 0.0395285i | ||||
\(641\) | 42.0000 | 1.65890 | 0.829450 | − | 0.558581i | \(-0.188654\pi\) | ||||
0.829450 | + | 0.558581i | \(0.188654\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 14.0000i | 0.552106i | 0.961142 | + | 0.276053i | \(0.0890266\pi\) | ||||
−0.961142 | + | 0.276053i | \(0.910973\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −28.0000 | −1.10165 | ||||||||
\(647\) | 23.0000i | 0.904223i | 0.891961 | + | 0.452112i | \(0.149329\pi\) | ||||
−0.891961 | + | 0.452112i | \(0.850671\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.00000 | 0.0785069 | ||||||||
\(650\) | 15.0000 | + | 20.0000i | 0.588348 | + | 0.784465i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 12.0000i | 0.469956i | ||||||||
\(653\) | − | 2.00000i | − | 0.0782660i | −0.999234 | − | 0.0391330i | \(-0.987540\pi\) | ||
0.999234 | − | 0.0391330i | \(-0.0124596\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.00000 | + | 8.00000i | −0.156293 | + | 0.312586i | ||||
\(656\) | 3.00000 | 0.117130 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | − | 1.00000i | − | 0.0389841i | ||||||
\(659\) | −36.0000 | −1.40236 | −0.701180 | − | 0.712984i | \(-0.747343\pi\) | ||||
−0.701180 | + | 0.712984i | \(0.747343\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 40.0000 | 1.55582 | 0.777910 | − | 0.628376i | \(-0.216280\pi\) | ||||
0.777910 | + | 0.628376i | \(0.216280\pi\) | |||||||
\(662\) | − | 12.0000i | − | 0.466393i | ||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −7.00000 | −0.271653 | ||||||||
\(665\) | −14.0000 | − | 7.00000i | −0.542897 | − | 0.271448i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | − | 20.0000i | − | 0.773823i | ||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 15.0000 | − | 30.0000i | 0.579501 | − | 1.15900i | ||||
\(671\) | 2.00000 | 0.0772091 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12.0000i | 0.462566i | 0.972887 | + | 0.231283i | \(0.0742923\pi\) | ||||
−0.972887 | + | 0.231283i | \(0.925708\pi\) | |||||||
\(674\) | 2.00000 | 0.0770371 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 12.0000 | 0.461538 | ||||||||
\(677\) | 12.0000i | 0.461197i | 0.973049 | + | 0.230599i | \(0.0740685\pi\) | ||||
−0.973049 | + | 0.230599i | \(0.925932\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 14.0000 | 0.537271 | ||||||||
\(680\) | −4.00000 | + | 8.00000i | −0.153393 | + | 0.306786i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 28.0000i | 1.07139i | 0.844411 | + | 0.535695i | \(0.179950\pi\) | ||||
−0.844411 | + | 0.535695i | \(0.820050\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 34.0000 | + | 17.0000i | 1.29907 | + | 0.649537i | ||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − | 11.0000i | − | 0.419371i | ||||||
\(689\) | 5.00000 | 0.190485 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.00000 | 0.266293 | 0.133146 | − | 0.991096i | \(-0.457492\pi\) | ||||
0.133146 | + | 0.991096i | \(0.457492\pi\) | |||||||
\(692\) | − | 14.0000i | − | 0.532200i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −28.0000 | −1.06287 | ||||||||
\(695\) | 20.0000 | − | 40.0000i | 0.758643 | − | 1.51729i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 12.0000i | 0.454532i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −4.00000 | + | 3.00000i | −0.151186 | + | 0.113389i | ||||
\(701\) | −48.0000 | −1.81293 | −0.906467 | − | 0.422276i | \(-0.861231\pi\) | ||||
−0.906467 | + | 0.422276i | \(0.861231\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 28.0000i | 1.05604i | ||||||||
\(704\) | 1.00000 | 0.0376889 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 6.00000 | 0.225813 | ||||||||
\(707\) | − | 5.00000i | − | 0.188044i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 17.0000 | 0.638448 | 0.319224 | − | 0.947679i | \(-0.396578\pi\) | ||||
0.319224 | + | 0.947679i | \(0.396578\pi\) | |||||||
\(710\) | 32.0000 | + | 16.0000i | 1.20094 | + | 0.600469i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1.00000i | 0.0374766i | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 10.0000 | + | 5.00000i | 0.373979 | + | 0.186989i | ||||
\(716\) | −7.00000 | −0.261602 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | − | 5.00000i | − | 0.186598i | ||||||
\(719\) | −50.0000 | −1.86469 | −0.932343 | − | 0.361576i | \(-0.882239\pi\) | ||||
−0.932343 | + | 0.361576i | \(0.882239\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.00000 | −0.223452 | ||||||||
\(722\) | − | 30.0000i | − | 1.11648i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 14.0000 | 0.520306 | ||||||||
\(725\) | 18.0000 | + | 24.0000i | 0.668503 | + | 0.891338i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 22.0000i | 0.815935i | 0.912996 | + | 0.407967i | \(0.133762\pi\) | ||||
−0.912996 | + | 0.407967i | \(0.866238\pi\) | |||||||
\(728\) | 5.00000i | 0.185312i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −11.0000 | + | 22.0000i | −0.407128 | + | 0.814257i | ||||
\(731\) | 44.0000 | 1.62740 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 21.0000i | − | 0.775653i | −0.921732 | − | 0.387826i | \(-0.873226\pi\) | ||
0.921732 | − | 0.387826i | \(-0.126774\pi\) | |||||||
\(734\) | −2.00000 | −0.0738213 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 15.0000i | − | 0.552532i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 52.0000 | 1.91285 | 0.956425 | − | 0.291977i | \(-0.0943129\pi\) | ||||
0.956425 | + | 0.291977i | \(0.0943129\pi\) | |||||||
\(740\) | 8.00000 | + | 4.00000i | 0.294086 | + | 0.147043i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1.00000i | 0.0367112i | ||||||||
\(743\) | − | 26.0000i | − | 0.953847i | −0.878945 | − | 0.476924i | \(-0.841752\pi\) | ||
0.878945 | − | 0.476924i | \(-0.158248\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 12.0000 | − | 24.0000i | 0.439646 | − | 0.879292i | ||||
\(746\) | −18.0000 | −0.659027 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 4.00000i | 0.146254i | ||||||||
\(749\) | −6.00000 | −0.219235 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −50.0000 | −1.82453 | −0.912263 | − | 0.409605i | \(-0.865667\pi\) | ||||
−0.912263 | + | 0.409605i | \(0.865667\pi\) | |||||||
\(752\) | − | 1.00000i | − | 0.0364662i | ||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 30.0000 | 1.09254 | ||||||||
\(755\) | −10.0000 | + | 20.0000i | −0.363937 | + | 0.727875i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8.00000i | 0.290765i | 0.989376 | + | 0.145382i | \(0.0464413\pi\) | ||||
−0.989376 | + | 0.145382i | \(0.953559\pi\) | |||||||
\(758\) | − | 10.0000i | − | 0.363216i | ||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −14.0000 | − | 7.00000i | −0.507833 | − | 0.253917i | ||||
\(761\) | −30.0000 | −1.08750 | −0.543750 | − | 0.839248i | \(-0.682996\pi\) | ||||
−0.543750 | + | 0.839248i | \(0.682996\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 15.0000i | 0.543036i | ||||||||
\(764\) | 11.0000 | 0.397966 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 10.0000i | 0.361079i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6.00000 | −0.216366 | −0.108183 | − | 0.994131i | \(-0.534503\pi\) | ||||
−0.108183 | + | 0.994131i | \(0.534503\pi\) | |||||||
\(770\) | −1.00000 | + | 2.00000i | −0.0360375 | + | 0.0720750i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 18.0000i | 0.647834i | ||||||||
\(773\) | − | 50.0000i | − | 1.79838i | −0.437564 | − | 0.899188i | \(-0.644158\pi\) | ||
0.437564 | − | 0.899188i | \(-0.355842\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 14.0000 | 0.502571 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 6.00000i | 0.215110i | ||||||||
\(779\) | −21.0000 | −0.752403 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 16.0000 | 0.572525 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1.00000 | −0.0357143 | ||||||||
\(785\) | 28.0000 | + | 14.0000i | 0.999363 | + | 0.499681i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 22.0000i | 0.784215i | 0.919919 | + | 0.392108i | \(0.128254\pi\) | ||||
−0.919919 | + | 0.392108i | \(0.871746\pi\) | |||||||
\(788\) | 15.0000i | 0.534353i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 20.0000 | + | 10.0000i | 0.711568 | + | 0.355784i | ||||
\(791\) | 15.0000 | 0.533339 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 10.0000i | 0.355110i | ||||||||
\(794\) | −34.0000 | −1.20661 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 7.00000 | 0.248108 | ||||||||
\(797\) | 48.0000i | 1.70025i | 0.526583 | + | 0.850124i | \(0.323473\pi\) | ||||
−0.526583 | + | 0.850124i | \(0.676527\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.00000 | 0.141510 | ||||||||
\(800\) | −4.00000 | + | 3.00000i | −0.141421 | + | 0.106066i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | − | 30.0000i | − | 1.05934i | ||||||
\(803\) | 11.0000i | 0.388182i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − | 5.00000i | − | 0.175899i | ||||||
\(809\) | 12.0000 | 0.421898 | 0.210949 | − | 0.977497i | \(-0.432345\pi\) | ||||
0.210949 | + | 0.977497i | \(0.432345\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −37.0000 | −1.29925 | −0.649623 | − | 0.760257i | \(-0.725073\pi\) | ||||
−0.649623 | + | 0.760257i | \(0.725073\pi\) | |||||||
\(812\) | 6.00000i | 0.210559i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 4.00000 | 0.140200 | ||||||||
\(815\) | −24.0000 | − | 12.0000i | −0.840683 | − | 0.420342i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 77.0000i | 2.69389i | ||||||||
\(818\) | 22.0000i | 0.769212i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −3.00000 | + | 6.00000i | −0.104765 | + | 0.209529i | ||||
\(821\) | −18.0000 | −0.628204 | −0.314102 | − | 0.949389i | \(-0.601703\pi\) | ||||
−0.314102 | + | 0.949389i | \(0.601703\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 17.0000i | − | 0.592583i | −0.955098 | − | 0.296291i | \(-0.904250\pi\) | ||
0.955098 | − | 0.296291i | \(-0.0957499\pi\) | |||||||
\(824\) | −6.00000 | −0.209020 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.00000 | −0.0695889 | ||||||||
\(827\) | − | 6.00000i | − | 0.208640i | −0.994544 | − | 0.104320i | \(-0.966733\pi\) | ||
0.994544 | − | 0.104320i | \(-0.0332667\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 34.0000 | 1.18087 | 0.590434 | − | 0.807086i | \(-0.298956\pi\) | ||||
0.590434 | + | 0.807086i | \(0.298956\pi\) | |||||||
\(830\) | 7.00000 | − | 14.0000i | 0.242974 | − | 0.485947i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 5.00000i | 0.173344i | ||||||||
\(833\) | − | 4.00000i | − | 0.138592i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 40.0000 | + | 20.0000i | 1.38426 | + | 0.692129i | ||||
\(836\) | −7.00000 | −0.242100 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − | 18.0000i | − | 0.621800i | ||||||
\(839\) | −46.0000 | −1.58810 | −0.794048 | − | 0.607855i | \(-0.792030\pi\) | ||||
−0.794048 | + | 0.607855i | \(0.792030\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.00000 | 0.241379 | ||||||||
\(842\) | 11.0000i | 0.379085i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −10.0000 | −0.344214 | ||||||||
\(845\) | −12.0000 | + | 24.0000i | −0.412813 | + | 0.825625i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 10.0000i | − | 0.343604i | ||||||
\(848\) | 1.00000i | 0.0343401i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −12.0000 | − | 16.0000i | −0.411597 | − | 0.548795i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 26.0000i | 0.890223i | 0.895475 | + | 0.445112i | \(0.146836\pi\) | ||||
−0.895475 | + | 0.445112i | \(0.853164\pi\) | |||||||
\(854\) | −2.00000 | −0.0684386 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −6.00000 | −0.205076 | ||||||||
\(857\) | 52.0000i | 1.77629i | 0.459567 | + | 0.888143i | \(0.348005\pi\) | ||||
−0.459567 | + | 0.888143i | \(0.651995\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −15.0000 | −0.511793 | −0.255897 | − | 0.966704i | \(-0.582371\pi\) | ||||
−0.255897 | + | 0.966704i | \(0.582371\pi\) | |||||||
\(860\) | 22.0000 | + | 11.0000i | 0.750194 | + | 0.375097i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 3.00000i | 0.102180i | ||||||||
\(863\) | − | 6.00000i | − | 0.204242i | −0.994772 | − | 0.102121i | \(-0.967437\pi\) | ||
0.994772 | − | 0.102121i | \(-0.0325630\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 28.0000 | + | 14.0000i | 0.952029 | + | 0.476014i | ||||
\(866\) | −17.0000 | −0.577684 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 10.0000 | 0.339227 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 75.0000 | 2.54128 | ||||||||
\(872\) | 15.0000i | 0.507964i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.00000 | − | 11.0000i | −0.0676123 | − | 0.371868i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 18.0000i | − | 0.607817i | −0.952701 | − | 0.303908i | \(-0.901708\pi\) | ||
0.952701 | − | 0.303908i | \(-0.0982917\pi\) | |||||||
\(878\) | − | 3.00000i | − | 0.101245i | ||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1.00000 | + | 2.00000i | −0.0337100 | + | 0.0674200i | ||||
\(881\) | −18.0000 | −0.606435 | −0.303218 | − | 0.952921i | \(-0.598061\pi\) | ||||
−0.303218 | + | 0.952921i | \(0.598061\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 20.0000i | 0.673054i | 0.941674 | + | 0.336527i | \(0.109252\pi\) | ||||
−0.941674 | + | 0.336527i | \(0.890748\pi\) | |||||||
\(884\) | −20.0000 | −0.672673 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −36.0000 | −1.20944 | ||||||||
\(887\) | 15.0000i | 0.503651i | 0.967773 | + | 0.251825i | \(0.0810309\pi\) | ||||
−0.967773 | + | 0.251825i | \(0.918969\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 9.00000 | 0.301850 | ||||||||
\(890\) | −2.00000 | − | 1.00000i | −0.0670402 | − | 0.0335201i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 14.0000i | 0.468755i | ||||||||
\(893\) | 7.00000i | 0.234246i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7.00000 | − | 14.0000i | 0.233984 | − | 0.467968i | ||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 18.0000i | 0.600668i | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.00000 | −0.133259 | ||||||||
\(902\) | 3.00000i | 0.0998891i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 15.0000 | 0.498893 | ||||||||
\(905\) | −14.0000 | + | 28.0000i | −0.465376 | + | 0.930751i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 31.0000i | 1.02934i | 0.857389 | + | 0.514669i | \(0.172085\pi\) | ||||
−0.857389 | + | 0.514669i | \(0.827915\pi\) | |||||||
\(908\) | 7.00000i | 0.232303i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −10.0000 | − | 5.00000i | −0.331497 | − | 0.165748i | ||||
\(911\) | 27.0000 | 0.894550 | 0.447275 | − | 0.894397i | \(-0.352395\pi\) | ||||
0.447275 | + | 0.894397i | \(0.352395\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 7.00000i | − | 0.231666i | ||||||
\(914\) | −22.0000 | −0.727695 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 14.0000 | 0.462573 | ||||||||
\(917\) | − | 4.00000i | − | 0.132092i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 46.0000 | 1.51740 | 0.758700 | − | 0.651440i | \(-0.225835\pi\) | ||||
0.758700 | + | 0.651440i | \(0.225835\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − | 15.0000i | − | 0.493999i | ||||||
\(923\) | 80.0000i | 2.63323i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −16.0000 | + | 12.0000i | −0.526077 | + | 0.394558i | ||||
\(926\) | −21.0000 | −0.690103 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 6.00000i | 0.196960i | ||||||||
\(929\) | −45.0000 | −1.47640 | −0.738201 | − | 0.674581i | \(-0.764324\pi\) | ||||
−0.738201 | + | 0.674581i | \(0.764324\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.00000 | 0.229416 | ||||||||
\(932\) | 3.00000i | 0.0982683i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −28.0000 | −0.916188 | ||||||||
\(935\) | −8.00000 | − | 4.00000i | −0.261628 | − | 0.130814i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 29.0000i | − | 0.947389i | −0.880689 | − | 0.473694i | \(-0.842920\pi\) | ||
0.880689 | − | 0.473694i | \(-0.157080\pi\) | |||||||
\(938\) | 15.0000i | 0.489767i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 2.00000 | + | 1.00000i | 0.0652328 | + | 0.0326164i | ||||
\(941\) | 33.0000 | 1.07577 | 0.537885 | − | 0.843018i | \(-0.319224\pi\) | ||||
0.537885 | + | 0.843018i | \(0.319224\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | −2.00000 | −0.0650945 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 11.0000 | 0.357641 | ||||||||
\(947\) | − | 30.0000i | − | 0.974869i | −0.873160 | − | 0.487435i | \(-0.837933\pi\) | ||
0.873160 | − | 0.487435i | \(-0.162067\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −55.0000 | −1.78538 | ||||||||
\(950\) | 28.0000 | − | 21.0000i | 0.908440 | − | 0.681330i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | − | 4.00000i | − | 0.129641i | ||||||
\(953\) | − | 6.00000i | − | 0.194359i | −0.995267 | − | 0.0971795i | \(-0.969018\pi\) | ||
0.995267 | − | 0.0971795i | \(-0.0309821\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −11.0000 | + | 22.0000i | −0.355952 | + | 0.711903i | ||||
\(956\) | 4.00000 | 0.129369 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 14.0000i | − | 0.452319i | ||||||
\(959\) | −17.0000 | −0.548959 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −31.0000 | −1.00000 | ||||||||
\(962\) | 20.0000i | 0.644826i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 10.0000 | 0.322078 | ||||||||
\(965\) | −36.0000 | − | 18.0000i | −1.15888 | − | 0.579441i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 3.00000i | − | 0.0964735i | −0.998836 | − | 0.0482367i | \(-0.984640\pi\) | ||
0.998836 | − | 0.0482367i | \(-0.0153602\pi\) | |||||||
\(968\) | − | 10.0000i | − | 0.321412i | ||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −14.0000 | + | 28.0000i | −0.449513 | + | 0.899026i | ||||
\(971\) | 30.0000 | 0.962746 | 0.481373 | − | 0.876516i | \(-0.340138\pi\) | ||||
0.481373 | + | 0.876516i | \(0.340138\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 20.0000i | 0.641171i | ||||||||
\(974\) | −33.0000 | −1.05739 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.00000 | −0.0640184 | ||||||||
\(977\) | − | 33.0000i | − | 1.05576i | −0.849318 | − | 0.527882i | \(-0.822986\pi\) | ||
0.849318 | − | 0.527882i | \(-0.177014\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.00000 | −0.0319601 | ||||||||
\(980\) | 1.00000 | − | 2.00000i | 0.0319438 | − | 0.0638877i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − | 36.0000i | − | 1.14881i | ||||||
\(983\) | 24.0000i | 0.765481i | 0.923856 | + | 0.382741i | \(0.125020\pi\) | ||||
−0.923856 | + | 0.382741i | \(0.874980\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −30.0000 | − | 15.0000i | −0.955879 | − | 0.477940i | ||||
\(986\) | −24.0000 | −0.764316 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − | 35.0000i | − | 1.11350i | ||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 60.0000 | 1.90596 | 0.952981 | − | 0.303029i | \(-0.0979978\pi\) | ||||
0.952981 | + | 0.303029i | \(0.0979978\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −16.0000 | −0.507489 | ||||||||
\(995\) | −7.00000 | + | 14.0000i | −0.221915 | + | 0.443830i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 2.00000i | − | 0.0633406i | −0.999498 | − | 0.0316703i | \(-0.989917\pi\) | ||
0.999498 | − | 0.0316703i | \(-0.0100827\pi\) | |||||||
\(998\) | − | 40.0000i | − | 1.26618i | ||||||
\(999\) | 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 | 1890.2.g.i.379.1 | yes | 2 | |
3.2 | odd | 2 | 1890.2.g.d.379.2 | yes | 2 | ||
5.2 | odd | 4 | 9450.2.a.ci.1.1 | 1 | |||
5.3 | odd | 4 | 9450.2.a.bk.1.1 | 1 | |||
5.4 | even | 2 | inner | 1890.2.g.i.379.2 | yes | 2 | |
15.2 | even | 4 | 9450.2.a.q.1.1 | 1 | |||
15.8 | even | 4 | 9450.2.a.dq.1.1 | 1 | |||
15.14 | odd | 2 | 1890.2.g.d.379.1 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1890.2.g.d.379.1 | ✓ | 2 | 15.14 | odd | 2 | ||
1890.2.g.d.379.2 | yes | 2 | 3.2 | odd | 2 | ||
1890.2.g.i.379.1 | yes | 2 | 1.1 | even | 1 | trivial | |
1890.2.g.i.379.2 | yes | 2 | 5.4 | even | 2 | inner | |
9450.2.a.q.1.1 | 1 | 15.2 | even | 4 | |||
9450.2.a.bk.1.1 | 1 | 5.3 | odd | 4 | |||
9450.2.a.ci.1.1 | 1 | 5.2 | odd | 4 | |||
9450.2.a.dq.1.1 | 1 | 15.8 | even | 4 |