Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4032,2,Mod(1583,4032)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4032, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3, 2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4032.1583");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4032 = 2^{6} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4032.v (of order \(4\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(32.1956820950\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(18\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 1008) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1583.17 | ||
Character | \(\chi\) | \(=\) | 4032.1583 |
Dual form | 4032.2.v.d.3599.17 |
$q$-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 \(\left(\mathbb{Z}/4032\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(1793\) | \(3781\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.53823 | + | 2.53823i | 1.13513 | + | 1.13513i | 0.989312 | + | 0.145817i | \(0.0465812\pi\) |
0.145817 | + | 0.989312i | \(0.453419\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.490893 | − | 0.490893i | 0.148010 | − | 0.148010i | −0.629219 | − | 0.777228i | \(-0.716625\pi\) |
0.777228 | + | 0.629219i | \(0.216625\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.21725 | − | 4.21725i | −1.16966 | − | 1.16966i | −0.982290 | − | 0.187366i | \(-0.940005\pi\) |
−0.187366 | − | 0.982290i | \(-0.559995\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.71835i | 1.62944i | 0.579856 | + | 0.814719i | \(0.303109\pi\) | ||||
−0.579856 | + | 0.814719i | \(0.696891\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.38631 | − | 5.38631i | 1.23570 | − | 1.23570i | 0.273965 | − | 0.961740i | \(-0.411665\pi\) |
0.961740 | − | 0.273965i | \(-0.0883351\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 1.37152i | − | 0.285981i | −0.989724 | − | 0.142990i | \(-0.954328\pi\) | ||
0.989724 | − | 0.142990i | \(-0.0456718\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 7.88518i | 1.57704i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.45725 | + | 1.45725i | −0.270604 | + | 0.270604i | −0.829343 | − | 0.558739i | \(-0.811285\pi\) |
0.558739 | + | 0.829343i | \(0.311285\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.66033i | 0.477809i | 0.971043 | + | 0.238905i | \(0.0767883\pi\) | ||||
−0.971043 | + | 0.238905i | \(0.923212\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.53823 | + | 2.53823i | 0.429038 | + | 0.429038i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.41550 | − | 2.41550i | 0.397106 | − | 0.397106i | −0.480105 | − | 0.877211i | \(-0.659401\pi\) |
0.877211 | + | 0.480105i | \(0.159401\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.51556 | −0.236690 | −0.118345 | − | 0.992973i | \(-0.537759\pi\) | ||||
−0.118345 | + | 0.992973i | \(0.537759\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.40983 | + | 3.40983i | 0.519994 | + | 0.519994i | 0.917570 | − | 0.397575i | \(-0.130148\pi\) |
−0.397575 | + | 0.917570i | \(0.630148\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 13.2646 | 1.93484 | 0.967418 | − | 0.253186i | \(-0.0814785\pi\) | ||||
0.967418 | + | 0.253186i | \(0.0814785\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.42484 | + | 9.42484i | 1.29460 | + | 1.29460i | 0.931909 | + | 0.362693i | \(0.118143\pi\) |
0.362693 | + | 0.931909i | \(0.381857\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.49199 | 0.336020 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.46141 | + | 5.46141i | −0.711015 | + | 0.711015i | −0.966748 | − | 0.255732i | \(-0.917683\pi\) |
0.255732 | + | 0.966748i | \(0.417683\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.16928 | + | 8.16928i | 1.04597 | + | 1.04597i | 0.998891 | + | 0.0470778i | \(0.0149909\pi\) |
0.0470778 | + | 0.998891i | \(0.485009\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 21.4087i | − | 2.65542i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.47267 | − | 2.47267i | 0.302084 | − | 0.302084i | −0.539745 | − | 0.841829i | \(-0.681479\pi\) |
0.841829 | + | 0.539745i | \(0.181479\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 9.71605i | − | 1.15308i | −0.817068 | − | 0.576541i | \(-0.804402\pi\) | ||
0.817068 | − | 0.576541i | \(-0.195598\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 2.38494i | − | 0.279136i | −0.990212 | − | 0.139568i | \(-0.955429\pi\) | ||
0.990212 | − | 0.139568i | \(-0.0445714\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.490893 | − | 0.490893i | 0.0559424 | − | 0.0559424i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.70360i | 0.529196i | 0.964359 | + | 0.264598i | \(0.0852393\pi\) | ||||
−0.964359 | + | 0.264598i | \(0.914761\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.75521 | + | 7.75521i | 0.851245 | + | 0.851245i | 0.990287 | − | 0.139042i | \(-0.0444022\pi\) |
−0.139042 | + | 0.990287i | \(0.544402\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −17.0527 | + | 17.0527i | −1.84962 | + | 1.84962i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.36941 | −0.569157 | −0.284578 | − | 0.958653i | \(-0.591854\pi\) | ||||
−0.284578 | + | 0.958653i | \(0.591854\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.21725 | − | 4.21725i | −0.442088 | − | 0.442088i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 27.3433 | 2.80537 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.44726 | −0.350016 | −0.175008 | − | 0.984567i | \(-0.555995\pi\) | ||||
−0.175008 | + | 0.984567i | \(0.555995\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.49553 | + | 2.49553i | 0.248314 | + | 0.248314i | 0.820279 | − | 0.571964i | \(-0.193818\pi\) |
−0.571964 | + | 0.820279i | \(0.693818\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.88100 | −0.776538 | −0.388269 | − | 0.921546i | \(-0.626927\pi\) | ||||
−0.388269 | + | 0.921546i | \(0.626927\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.26289 | − | 2.26289i | 0.218761 | − | 0.218761i | −0.589215 | − | 0.807976i | \(-0.700563\pi\) |
0.807976 | + | 0.589215i | \(0.200563\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.64611 | + | 7.64611i | 0.732365 | + | 0.732365i | 0.971088 | − | 0.238723i | \(-0.0767288\pi\) |
−0.238723 | + | 0.971088i | \(0.576729\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.74388i | 0.352194i | 0.984373 | + | 0.176097i | \(0.0563473\pi\) | ||||
−0.984373 | + | 0.176097i | \(0.943653\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.48122 | − | 3.48122i | 0.324625 | − | 0.324625i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.71835i | 0.615870i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.5180i | 0.956186i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −7.32323 | + | 7.32323i | −0.655010 | + | 0.655010i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 12.6076i | − | 1.11875i | −0.828916 | − | 0.559373i | \(-0.811042\pi\) | ||
0.828916 | − | 0.559373i | \(-0.188958\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.9113 | + | 10.9113i | 0.953325 | + | 0.953325i | 0.998958 | − | 0.0456330i | \(-0.0145305\pi\) |
−0.0456330 | + | 0.998958i | \(0.514530\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.38631 | − | 5.38631i | 0.467052 | − | 0.467052i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −8.84548 | −0.755720 | −0.377860 | − | 0.925863i | \(-0.623340\pi\) | ||||
−0.377860 | + | 0.925863i | \(0.623340\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.85221 | − | 5.85221i | −0.496378 | − | 0.496378i | 0.413930 | − | 0.910309i | \(-0.364156\pi\) |
−0.910309 | + | 0.413930i | \(0.864156\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.14044 | −0.346241 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −7.39764 | −0.614340 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.71683 | + | 4.71683i | 0.386418 | + | 0.386418i | 0.873408 | − | 0.486990i | \(-0.161905\pi\) |
−0.486990 | + | 0.873408i | \(0.661905\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −10.6200 | −0.864246 | −0.432123 | − | 0.901815i | \(-0.642235\pi\) | ||||
−0.432123 | + | 0.901815i | \(0.642235\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.75251 | + | 6.75251i | −0.542375 | + | 0.542375i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −12.6976 | − | 12.6976i | −1.01338 | − | 1.01338i | −0.999909 | − | 0.0134693i | \(-0.995712\pi\) |
−0.0134693 | − | 0.999909i | \(-0.504288\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 1.37152i | − | 0.108091i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −17.2947 | + | 17.2947i | −1.35462 | + | 1.35462i | −0.474215 | + | 0.880409i | \(0.657268\pi\) |
−0.880409 | + | 0.474215i | \(0.842732\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 18.1120i | − | 1.40155i | −0.713382 | − | 0.700776i | \(-0.752837\pi\) | ||
0.713382 | − | 0.700776i | \(-0.247163\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 22.5705i | 1.73619i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 7.32043 | − | 7.32043i | 0.556562 | − | 0.556562i | −0.371765 | − | 0.928327i | \(-0.621247\pi\) |
0.928327 | + | 0.371765i | \(0.121247\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 7.88518i | 0.596063i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −10.7625 | − | 10.7625i | −0.804427 | − | 0.804427i | 0.179357 | − | 0.983784i | \(-0.442598\pi\) |
−0.983784 | + | 0.179357i | \(0.942598\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.0479 | + | 10.0479i | −0.746855 | + | 0.746855i | −0.973887 | − | 0.227033i | \(-0.927098\pi\) |
0.227033 | + | 0.973887i | \(0.427098\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 12.2622 | 0.901533 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.29799 | + | 3.29799i | 0.241173 | + | 0.241173i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −19.9473 | −1.44334 | −0.721670 | − | 0.692238i | \(-0.756625\pi\) | ||||
−0.721670 | + | 0.692238i | \(0.756625\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −14.6426 | −1.05400 | −0.527000 | − | 0.849865i | \(-0.676683\pi\) | ||||
−0.527000 | + | 0.849865i | \(0.676683\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.16271 | − | 2.16271i | −0.154087 | − | 0.154087i | 0.625854 | − | 0.779941i | \(-0.284751\pi\) |
−0.779941 | + | 0.625854i | \(0.784751\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.68951 | 0.615983 | 0.307991 | − | 0.951389i | \(-0.400343\pi\) | ||||
0.307991 | + | 0.951389i | \(0.400343\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.45725 | + | 1.45725i | −0.102279 | + | 0.102279i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.84682 | − | 3.84682i | −0.268674 | − | 0.268674i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 5.28820i | − | 0.365792i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.21024 | + | 1.21024i | −0.0833164 | + | 0.0833164i | −0.747537 | − | 0.664220i | \(-0.768764\pi\) |
0.664220 | + | 0.747537i | \(0.268764\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 17.3098i | 1.18052i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.66033i | 0.180595i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 28.3330 | − | 28.3330i | 1.90588 | − | 1.90588i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.184249i | 0.0123382i | 0.999981 | + | 0.00616910i | \(0.00196370\pi\) | ||||
−0.999981 | + | 0.00616910i | \(0.998036\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5.79571 | − | 5.79571i | −0.384675 | − | 0.384675i | 0.488108 | − | 0.872783i | \(-0.337687\pi\) |
−0.872783 | + | 0.488108i | \(0.837687\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 15.7114 | − | 15.7114i | 1.03824 | − | 1.03824i | 0.0390024 | − | 0.999239i | \(-0.487582\pi\) |
0.999239 | − | 0.0390024i | \(-0.0124180\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −9.79337 | −0.641585 | −0.320793 | − | 0.947149i | \(-0.603949\pi\) | ||||
−0.320793 | + | 0.947149i | \(0.603949\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 33.6684 | + | 33.6684i | 2.19629 | + | 2.19629i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 15.0153 | 0.971257 | 0.485629 | − | 0.874165i | \(-0.338591\pi\) | ||||
0.485629 | + | 0.874165i | \(0.338591\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 21.6047 | 1.39168 | 0.695841 | − | 0.718196i | \(-0.255032\pi\) | ||||
0.695841 | + | 0.718196i | \(0.255032\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.53823 | + | 2.53823i | 0.162161 | + | 0.162161i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −45.4309 | −2.89070 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 14.9759 | − | 14.9759i | 0.945269 | − | 0.945269i | −0.0533095 | − | 0.998578i | \(-0.516977\pi\) |
0.998578 | + | 0.0533095i | \(0.0169770\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.673267 | − | 0.673267i | −0.0423279 | − | 0.0423279i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 8.05949i | − | 0.502737i | −0.967891 | − | 0.251369i | \(-0.919119\pi\) | ||
0.967891 | − | 0.251369i | \(-0.0808807\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.41550 | − | 2.41550i | 0.150092 | − | 0.150092i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 15.9502i | 0.983531i | 0.870728 | + | 0.491766i | \(0.163648\pi\) | ||||
−0.870728 | + | 0.491766i | \(0.836352\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 47.8448i | 2.93908i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.75178 | + | 2.75178i | −0.167779 | + | 0.167779i | −0.786002 | − | 0.618223i | \(-0.787853\pi\) |
0.618223 | + | 0.786002i | \(0.287853\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 2.32138i | − | 0.141014i | −0.997511 | − | 0.0705070i | \(-0.977538\pi\) | ||
0.997511 | − | 0.0705070i | \(-0.0224617\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.87077 | + | 3.87077i | 0.233416 | + | 0.233416i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.66939 | − | 9.66939i | 0.580977 | − | 0.580977i | −0.354194 | − | 0.935172i | \(-0.615245\pi\) |
0.935172 | + | 0.354194i | \(0.115245\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 24.1266 | 1.43927 | 0.719637 | − | 0.694351i | \(-0.244308\pi\) | ||||
0.719637 | + | 0.694351i | \(0.244308\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.5365 | + | 15.5365i | 0.923547 | + | 0.923547i | 0.997278 | − | 0.0737311i | \(-0.0234907\pi\) |
−0.0737311 | + | 0.997278i | \(0.523491\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.51556 | −0.0894604 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −28.1362 | −1.65507 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3.43691 | + | 3.43691i | 0.200787 | + | 0.200787i | 0.800337 | − | 0.599550i | \(-0.204654\pi\) |
−0.599550 | + | 0.800337i | \(0.704654\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −27.7246 | −1.61419 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −5.78403 | + | 5.78403i | −0.334499 | + | 0.334499i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.40983 | + | 3.40983i | 0.196539 | + | 0.196539i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 41.4709i | 2.37462i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −21.6774 | + | 21.6774i | −1.23719 | + | 1.23719i | −0.276050 | + | 0.961143i | \(0.589026\pi\) |
−0.961143 | + | 0.276050i | \(0.910974\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 22.3827i | − | 1.26920i | −0.772839 | − | 0.634602i | \(-0.781164\pi\) | ||
0.772839 | − | 0.634602i | \(-0.218836\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 18.7841i | 1.06174i | 0.847454 | + | 0.530869i | \(0.178134\pi\) | ||||
−0.847454 | + | 0.530869i | \(0.821866\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 10.4581 | − | 10.4581i | 0.587388 | − | 0.587388i | −0.349535 | − | 0.936923i | \(-0.613660\pi\) |
0.936923 | + | 0.349535i | \(0.113660\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.43070i | 0.0801040i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 36.1871 | + | 36.1871i | 2.01350 | + | 2.01350i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 33.2538 | − | 33.2538i | 1.84459 | − | 1.84459i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 13.2646 | 0.731299 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.13347 | + | 2.13347i | 0.117266 | + | 0.117266i | 0.763305 | − | 0.646038i | \(-0.223575\pi\) |
−0.646038 | + | 0.763305i | \(0.723575\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 12.5524 | 0.685809 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.08023 | 0.440158 | 0.220079 | − | 0.975482i | \(-0.429368\pi\) | ||||
0.220079 | + | 0.975482i | \(0.429368\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.30594 | + | 1.30594i | 0.0707204 | + | 0.0707204i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.45329 | − | 2.45329i | 0.131699 | − | 0.131699i | −0.638184 | − | 0.769884i | \(-0.720314\pi\) |
0.769884 | + | 0.638184i | \(0.220314\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −18.5622 | − | 18.5622i | −0.993612 | − | 0.993612i | 0.00636783 | − | 0.999980i | \(-0.497973\pi\) |
−0.999980 | + | 0.00636783i | \(0.997973\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 13.7220i | 0.730348i | 0.930939 | + | 0.365174i | \(0.118991\pi\) | ||||
−0.930939 | + | 0.365174i | \(0.881009\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 24.6615 | − | 24.6615i | 1.30890 | − | 1.30890i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 1.64418i | − | 0.0867763i | −0.999058 | − | 0.0433881i | \(-0.986185\pi\) | ||
0.999058 | − | 0.0433881i | \(-0.0138152\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 39.0247i | − | 2.05393i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.05351 | − | 6.05351i | 0.316855 | − | 0.316855i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 30.8382i | − | 1.60974i | −0.593449 | − | 0.804871i | \(-0.702234\pi\) | ||
0.593449 | − | 0.804871i | \(-0.297766\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 9.42484 | + | 9.42484i | 0.489313 | + | 0.489313i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.20792 | − | 4.20792i | 0.217878 | − | 0.217878i | −0.589726 | − | 0.807604i | \(-0.700764\pi\) |
0.807604 | + | 0.589726i | \(0.200764\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 12.2912 | 0.633027 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.62605 | + | 1.62605i | 0.0835245 | + | 0.0835245i | 0.747635 | − | 0.664110i | \(-0.231189\pi\) |
−0.664110 | + | 0.747635i | \(0.731189\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −13.9352 | −0.712053 | −0.356027 | − | 0.934476i | \(-0.615869\pi\) | ||||
−0.356027 | + | 0.934476i | \(0.615869\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.49199 | 0.127004 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 24.4433 | + | 24.4433i | 1.23933 | + | 1.23933i | 0.960277 | + | 0.279048i | \(0.0900188\pi\) |
0.279048 | + | 0.960277i | \(0.409981\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.21432 | 0.465988 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −11.9388 | + | 11.9388i | −0.600706 | + | 0.600706i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 19.0249 | + | 19.0249i | 0.954832 | + | 0.954832i | 0.999023 | − | 0.0441916i | \(-0.0140712\pi\) |
−0.0441916 | + | 0.999023i | \(0.514071\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.40410i | 0.269868i | 0.990855 | + | 0.134934i | \(0.0430822\pi\) | ||||
−0.990855 | + | 0.134934i | \(0.956918\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 11.2193 | − | 11.2193i | 0.558872 | − | 0.558872i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 2.37150i | − | 0.117551i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 13.2695i | − | 0.656134i | −0.944655 | − | 0.328067i | \(-0.893603\pi\) | ||
0.944655 | − | 0.328067i | \(-0.106397\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −5.46141 | + | 5.46141i | −0.268739 | + | 0.268739i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 39.3689i | 1.93255i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3.63116 | + | 3.63116i | 0.177394 | + | 0.177394i | 0.790219 | − | 0.612825i | \(-0.209967\pi\) |
−0.612825 | + | 0.790219i | \(0.709967\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 23.9365 | − | 23.9365i | 1.16659 | − | 1.16659i | 0.183592 | − | 0.983002i | \(-0.441227\pi\) |
0.983002 | − | 0.183592i | \(-0.0587726\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −52.9753 | −2.56968 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.16928 | + | 8.16928i | 0.395339 | + | 0.395339i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −21.6203 | −1.04141 | −0.520707 | − | 0.853736i | \(-0.674331\pi\) | ||||
−0.520707 | + | 0.853736i | \(0.674331\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.44643 | −0.261739 | −0.130869 | − | 0.991400i | \(-0.541777\pi\) | ||||
−0.130869 | + | 0.991400i | \(0.541777\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −7.38741 | − | 7.38741i | −0.353388 | − | 0.353388i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.74327 | 0.417294 | 0.208647 | − | 0.977991i | \(-0.433094\pi\) | ||||
0.208647 | + | 0.977991i | \(0.433094\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −16.3728 | + | 16.3728i | −0.777895 | + | 0.777895i | −0.979473 | − | 0.201578i | \(-0.935393\pi\) |
0.201578 | + | 0.979473i | \(0.435393\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −13.6288 | − | 13.6288i | −0.646066 | − | 0.646066i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 22.6779i | − | 1.07024i | −0.844777 | − | 0.535118i | \(-0.820267\pi\) | ||
0.844777 | − | 0.535118i | \(-0.179733\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.743975 | + | 0.743975i | −0.0350324 | + | 0.0350324i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 21.4087i | − | 1.00365i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 17.4655i | − | 0.817001i | −0.912758 | − | 0.408501i | \(-0.866052\pi\) | ||
0.912758 | − | 0.408501i | \(-0.133948\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.90382 | + | 3.90382i | −0.181819 | + | 0.181819i | −0.792148 | − | 0.610329i | \(-0.791037\pi\) |
0.610329 | + | 0.792148i | \(0.291037\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 1.25985i | − | 0.0585503i | −0.999571 | − | 0.0292752i | \(-0.990680\pi\) | ||
0.999571 | − | 0.0292752i | \(-0.00931990\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −9.48649 | − | 9.48649i | −0.438982 | − | 0.438982i | 0.452687 | − | 0.891669i | \(-0.350465\pi\) |
−0.891669 | + | 0.452687i | \(0.850465\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.47267 | − | 2.47267i | 0.114177 | − | 0.114177i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.34772 | 0.153928 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 42.4720 | + | 42.4720i | 1.94875 | + | 1.94875i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −6.08989 | −0.278254 | −0.139127 | − | 0.990275i | \(-0.544430\pi\) | ||||
−0.139127 | + | 0.990275i | \(0.544430\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −20.3736 | −0.928955 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −8.74992 | − | 8.74992i | −0.397313 | − | 0.397313i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −25.6331 | −1.16155 | −0.580773 | − | 0.814066i | \(-0.697249\pi\) | ||||
−0.580773 | + | 0.814066i | \(0.697249\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10.0392 | − | 10.0392i | 0.453062 | − | 0.453062i | −0.443308 | − | 0.896370i | \(-0.646195\pi\) |
0.896370 | + | 0.443308i | \(0.146195\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −9.79028 | − | 9.79028i | −0.440932 | − | 0.440932i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 9.71605i | − | 0.435824i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 25.2497 | − | 25.2497i | 1.13033 | − | 1.13033i | 0.140212 | − | 0.990122i | \(-0.455222\pi\) |
0.990122 | − | 0.140212i | \(-0.0447784\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 26.9906i | − | 1.20345i | −0.798702 | − | 0.601727i | \(-0.794480\pi\) | ||
0.798702 | − | 0.601727i | \(-0.205520\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 12.6684i | 0.563738i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 7.51549 | − | 7.51549i | 0.333118 | − | 0.333118i | −0.520651 | − | 0.853769i | \(-0.674311\pi\) |
0.853769 | + | 0.520651i | \(0.174311\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 2.38494i | − | 0.105503i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −20.0038 | − | 20.0038i | −0.881471 | − | 0.881471i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.51147 | − | 6.51147i | 0.286374 | − | 0.286374i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −16.3971 | −0.718372 | −0.359186 | − | 0.933266i | \(-0.616946\pi\) | ||||
−0.359186 | + | 0.933266i | \(0.616946\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −23.6070 | − | 23.6070i | −1.03226 | − | 1.03226i | −0.999462 | − | 0.0328016i | \(-0.989557\pi\) |
−0.0328016 | − | 0.999462i | \(-0.510443\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −17.8730 | −0.778560 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 21.1189 | 0.918215 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.39148 | + | 6.39148i | 0.276846 | + | 0.276846i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 11.4874 | 0.496645 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.490893 | − | 0.490893i | 0.0211442 | − | 0.0211442i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.00348 | + | 3.00348i | 0.129130 | + | 0.129130i | 0.768718 | − | 0.639588i | \(-0.220895\pi\) |
−0.639588 | + | 0.768718i | \(0.720895\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 38.8151i | 1.66266i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −13.5039 | + | 13.5039i | −0.577384 | + | 0.577384i | −0.934182 | − | 0.356797i | \(-0.883869\pi\) |
0.356797 | + | 0.934182i | \(0.383869\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 15.6984i | 0.668773i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.70360i | 0.200017i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −15.0607 | + | 15.0607i | −0.638143 | + | 0.638143i | −0.950097 | − | 0.311954i | \(-0.899016\pi\) |
0.311954 | + | 0.950097i | \(0.399016\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 28.7602i | − | 1.21643i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 11.0288 | + | 11.0288i | 0.464807 | + | 0.464807i | 0.900227 | − | 0.435420i | \(-0.143400\pi\) |
−0.435420 | + | 0.900227i | \(0.643400\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9.50281 | + | 9.50281i | −0.399786 | + | 0.399786i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3.00762 | 0.126086 | 0.0630430 | − | 0.998011i | \(-0.479919\pi\) | ||||
0.0630430 | + | 0.998011i | \(0.479919\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −15.1905 | − | 15.1905i | −0.635703 | − | 0.635703i | 0.313790 | − | 0.949493i | \(-0.398401\pi\) |
−0.949493 | + | 0.313790i | \(0.898401\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 10.8146 | 0.451002 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 0.322228 | 0.0134145 | 0.00670727 | − | 0.999978i | \(-0.497865\pi\) | ||||
0.00670727 | + | 0.999978i | \(0.497865\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7.75521 | + | 7.75521i | 0.321740 | + | 0.321740i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9.25317 | 0.383227 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −21.1091 | + | 21.1091i | −0.871266 | + | 0.871266i | −0.992610 | − | 0.121344i | \(-0.961279\pi\) |
0.121344 | + | 0.992610i | \(0.461279\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 14.3294 | + | 14.3294i | 0.590431 | + | 0.590431i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 7.41539i | 0.304514i | 0.988341 | + | 0.152257i | \(0.0486541\pi\) | ||||
−0.988341 | + | 0.152257i | \(0.951346\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −17.0527 | + | 17.0527i | −0.699092 | + | 0.699092i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 25.2627i | 1.03221i | 0.856526 | + | 0.516104i | \(0.172618\pi\) | ||||
−0.856526 | + | 0.516104i | \(0.827382\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.95409i | 0.242872i | 0.992599 | + | 0.121436i | \(0.0387500\pi\) | ||||
−0.992599 | + | 0.121436i | \(0.961250\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −26.6972 | + | 26.6972i | −1.08539 | + | 1.08539i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 39.7459i | − | 1.61324i | −0.591073 | − | 0.806618i | \(-0.701296\pi\) | ||
0.591073 | − | 0.806618i | \(-0.298704\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −55.9400 | − | 55.9400i | −2.26309 | − | 2.26309i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −21.8646 | + | 21.8646i | −0.883103 | + | 0.883103i | −0.993849 | − | 0.110746i | \(-0.964676\pi\) |
0.110746 | + | 0.993849i | \(0.464676\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −14.1189 | −0.568405 | −0.284202 | − | 0.958764i | \(-0.591729\pi\) | ||||
−0.284202 | + | 0.958764i | \(0.591729\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.98080 | + | 2.98080i | 0.119809 | + | 0.119809i | 0.764469 | − | 0.644660i | \(-0.223001\pi\) |
−0.644660 | + | 0.764469i | \(0.723001\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −5.36941 | −0.215121 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.24986 | 0.0899946 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 16.2282 | + | 16.2282i | 0.647060 | + | 0.647060i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 21.9208 | 0.872654 | 0.436327 | − | 0.899788i | \(-0.356279\pi\) | ||||
0.436327 | + | 0.899788i | \(0.356279\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 32.0010 | − | 32.0010i | 1.26992 | − | 1.26992i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.21725 | − | 4.21725i | −0.167094 | − | 0.167094i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.74291i | 0.266329i | 0.991094 | + | 0.133164i | \(0.0425139\pi\) | ||||
−0.991094 | + | 0.133164i | \(0.957486\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −8.56927 | + | 8.56927i | −0.337939 | + | 0.337939i | −0.855591 | − | 0.517652i | \(-0.826806\pi\) |
0.517652 | + | 0.855591i | \(0.326806\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 39.6964i | − | 1.56063i | −0.625389 | − | 0.780313i | \(-0.715060\pi\) | ||
0.625389 | − | 0.780313i | \(-0.284940\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.36193i | 0.210474i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.80312 | + | 1.80312i | −0.0705614 | + | 0.0705614i | −0.741507 | − | 0.670945i | \(-0.765888\pi\) |
0.670945 | + | 0.741507i | \(0.265888\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 55.3907i | 2.16429i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.79636 | + | 2.79636i | 0.108931 | + | 0.108931i | 0.759471 | − | 0.650541i | \(-0.225458\pi\) |
−0.650541 | + | 0.759471i | \(0.725458\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.53027 | + | 1.53027i | −0.0595205 | + | 0.0595205i | −0.736241 | − | 0.676720i | \(-0.763401\pi\) |
0.676720 | + | 0.736241i | \(0.263401\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 27.3433 | 1.06033 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.99864 | + | 1.99864i | 0.0773875 | + | 0.0773875i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 8.02048 | 0.309627 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −50.8286 | −1.95930 | −0.979649 | − | 0.200720i | \(-0.935672\pi\) | ||||
−0.979649 | + | 0.200720i | \(0.935672\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.52373 | + | 1.52373i | 0.0585617 | + | 0.0585617i | 0.735781 | − | 0.677219i | \(-0.236815\pi\) |
−0.677219 | + | 0.735781i | \(0.736815\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.44726 | −0.132294 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −0.480063 | + | 0.480063i | −0.0183691 | + | 0.0183691i | −0.716232 | − | 0.697863i | \(-0.754135\pi\) |
0.697863 | + | 0.716232i | \(0.254135\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −22.4518 | − | 22.4518i | −0.857840 | − | 0.857840i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 79.4939i | − | 3.02848i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 26.4280 | − | 26.4280i | 1.00537 | − | 1.00537i | 0.00538425 | − | 0.999986i | \(-0.498286\pi\) |
0.999986 | − | 0.00538425i | \(-0.00171387\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 29.7085i | − | 1.12691i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 10.1820i | − | 0.385672i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.40089 | − | 2.40089i | 0.0906804 | − | 0.0906804i | −0.660311 | − | 0.750992i | \(-0.729576\pi\) |
0.750992 | + | 0.660311i | \(0.229576\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 26.0213i | − | 0.981411i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.49553 | + | 2.49553i | 0.0938540 | + | 0.0938540i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 27.3668 | − | 27.3668i | 1.02778 | − | 1.02778i | 0.0281790 | − | 0.999603i | \(-0.491029\pi\) |
0.999603 | − | 0.0281790i | \(-0.00897084\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3.64868 | 0.136644 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −10.5094 | − | 10.5094i | −0.393028 | − | 0.393028i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 16.6007 | 0.619101 | 0.309551 | − | 0.950883i | \(-0.399821\pi\) | ||||
0.309551 | + | 0.950883i | \(0.399821\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.88100 | −0.293504 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −11.4906 | − | 11.4906i | −0.426752 | − | 0.426752i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 11.7244 | 0.434835 | 0.217418 | − | 0.976079i | \(-0.430237\pi\) | ||||
0.217418 | + | 0.976079i | \(0.430237\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −22.9084 | + | 22.9084i | −0.847298 | + | 0.847298i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −15.3078 | − | 15.3078i | −0.565407 | − | 0.565407i | 0.365431 | − | 0.930838i | \(-0.380921\pi\) |
−0.930838 | + | 0.365431i | \(0.880921\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 2.42763i | − | 0.0894228i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −21.4937 | + | 21.4937i | −0.790659 | + | 0.790659i | −0.981601 | − | 0.190942i | \(-0.938846\pi\) |
0.190942 | + | 0.981601i | \(0.438846\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 31.6334i | 1.16052i | 0.814432 | + | 0.580259i | \(0.197049\pi\) | ||||
−0.814432 | + | 0.580259i | \(0.802951\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 23.9448i | 0.877269i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.26289 | − | 2.26289i | 0.0826840 | − | 0.0826840i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 25.7604i | − | 0.940011i | −0.882663 | − | 0.470006i | \(-0.844252\pi\) | ||
0.882663 | − | 0.470006i | \(-0.155748\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −26.9560 | − | 26.9560i | −0.981031 | − | 0.981031i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 18.8485 | − | 18.8485i | 0.685061 | − | 0.685061i | −0.276075 | − | 0.961136i | \(-0.589034\pi\) |
0.961136 | + | 0.276075i | \(0.0890337\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3.04604 | 0.110419 | 0.0552094 | − | 0.998475i | \(-0.482417\pi\) | ||||
0.0552094 | + | 0.998475i | \(0.482417\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.64611 | + | 7.64611i | 0.276808 | + | 0.276808i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 46.0643 | 1.66329 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 7.94309 | 0.286435 | 0.143218 | − | 0.989691i | \(-0.454255\pi\) | ||||
0.143218 | + | 0.989691i | \(0.454255\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −19.3102 | − | 19.3102i | −0.694541 | − | 0.694541i | 0.268687 | − | 0.963228i | \(-0.413410\pi\) |
−0.963228 | + | 0.268687i | \(0.913410\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −20.9772 | −0.753522 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −8.16325 | + | 8.16325i | −0.292479 | + | 0.292479i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.76954 | − | 4.76954i | −0.170667 | − | 0.170667i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 64.4587i | − | 2.30063i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −20.2277 | + | 20.2277i | −0.721041 | + | 0.721041i | −0.968817 | − | 0.247777i | \(-0.920300\pi\) |
0.247777 | + | 0.968817i | \(0.420300\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.74388i | 0.133117i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 68.9039i | − | 2.44685i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 27.0767 | − | 27.0767i | 0.959105 | − | 0.959105i | −0.0400908 | − | 0.999196i | \(-0.512765\pi\) |
0.999196 | + | 0.0400908i | \(0.0127647\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 89.1159i | 3.15269i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.17075 | − | 1.17075i | −0.0413148 | − | 0.0413148i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.48122 | − | 3.48122i | 0.122697 | − | 0.122697i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −51.2572 | −1.80211 | −0.901054 | − | 0.433706i | \(-0.857206\pi\) | ||||
−0.901054 | + | 0.433706i | \(0.857206\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −15.6365 | − | 15.6365i | −0.549073 | − | 0.549073i | 0.377099 | − | 0.926173i | \(-0.376921\pi\) |
−0.926173 | + | 0.377099i | \(0.876921\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −87.7956 | −3.07535 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 36.7328 | 1.28512 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −11.0162 | − | 11.0162i | −0.384467 | − | 0.384467i | 0.488241 | − | 0.872709i | \(-0.337639\pi\) |
−0.872709 | + | 0.488241i | \(0.837639\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −34.8795 | −1.21582 | −0.607911 | − | 0.794005i | \(-0.707992\pi\) | ||||
−0.607911 | + | 0.794005i | \(0.707992\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −9.95741 | + | 9.95741i | −0.346253 | + | 0.346253i | −0.858712 | − | 0.512459i | \(-0.828735\pi\) |
0.512459 | + | 0.858712i | \(0.328735\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −19.7239 | − | 19.7239i | −0.685041 | − | 0.685041i | 0.276091 | − | 0.961132i | \(-0.410961\pi\) |
−0.961132 | + | 0.276091i | \(0.910961\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.71835i | 0.232777i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 45.9724 | − | 45.9724i | 1.59094 | − | 1.59094i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 17.7923i | − | 0.614257i | −0.951668 | − | 0.307129i | \(-0.900632\pi\) | ||
0.951668 | − | 0.307129i | \(-0.0993682\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 24.7529i | 0.853547i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −57.2890 | + | 57.2890i | −1.97080 | + | 1.97080i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 10.5180i | 0.361404i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.31290 | − | 3.31290i | −0.113565 | − | 0.113565i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −15.5555 | + | 15.5555i | −0.532610 | + | 0.532610i | −0.921348 | − | 0.388738i | \(-0.872911\pi\) |
0.388738 | + | 0.921348i | \(0.372911\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −55.7987 | −1.90605 | −0.953023 | − | 0.302898i | \(-0.902046\pi\) | ||||
−0.953023 | + | 0.302898i | \(0.902046\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −5.54812 | − | 5.54812i | −0.189299 | − | 0.189299i | 0.606094 | − | 0.795393i | \(-0.292736\pi\) |
−0.795393 | + | 0.606094i | \(0.792736\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 4.67668 | 0.159196 | 0.0795980 | − | 0.996827i | \(-0.474636\pi\) | ||||
0.0795980 | + | 0.996827i | \(0.474636\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 37.1618 | 1.26354 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.30896 | + | 2.30896i | 0.0783261 | + | 0.0783261i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −20.8557 | −0.706670 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −7.32323 | + | 7.32323i | −0.247570 | + | 0.247570i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 30.6084 | + | 30.6084i | 1.03357 | + | 1.03357i | 0.999417 | + | 0.0341550i | \(0.0108740\pi\) |
0.0341550 | + | 0.999417i | \(0.489126\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 4.23931i | − | 0.142826i | −0.997447 | − | 0.0714129i | \(-0.977249\pi\) | ||
0.997447 | − | 0.0714129i | \(-0.0227508\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 27.7473 | − | 27.7473i | 0.933772 | − | 0.933772i | −0.0641668 | − | 0.997939i | \(-0.520439\pi\) |
0.997939 | + | 0.0641668i | \(0.0204390\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 46.9699i | − | 1.57710i | −0.614973 | − | 0.788548i | \(-0.710833\pi\) | ||
0.614973 | − | 0.788548i | \(-0.289167\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 12.6076i | − | 0.422846i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 71.4470 | − | 71.4470i | 2.39088 | − | 2.39088i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 54.6353i | − | 1.82626i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3.87675 | − | 3.87675i | −0.129297 | − | 0.129297i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −63.3193 | + | 63.3193i | −2.10947 | + | 2.10947i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −51.0077 | −1.69555 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 10.5685 | + | 10.5685i | 0.350923 | + | 0.350923i | 0.860453 | − | 0.509530i | \(-0.170181\pi\) |
−0.509530 | + | 0.860453i | \(0.670181\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −25.9324 | −0.859180 | −0.429590 | − | 0.903024i | \(-0.641342\pi\) | ||||
−0.429590 | + | 0.903024i | \(0.641342\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7.61395 | 0.251985 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 10.9113 | + | 10.9113i | 0.360323 | + | 0.360323i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.79979 | −0.0593697 | −0.0296848 | − | 0.999559i | \(-0.509450\pi\) | ||||
−0.0296848 | + | 0.999559i | \(0.509450\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −40.9751 | + | 40.9751i | −1.34871 | + | 1.34871i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 19.0467 | + | 19.0467i | 0.626250 | + | 0.626250i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 21.4683i | − | 0.704353i | −0.935934 | − | 0.352176i | \(-0.885442\pi\) | ||
0.935934 | − | 0.352176i | \(-0.114558\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.38631 | − | 5.38631i | 0.176529 | − | 0.176529i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 16.7421i | 0.547524i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 14.6323i | 0.478016i | 0.971018 | + | 0.239008i | \(0.0768223\pi\) | ||||
−0.971018 | + | 0.239008i | \(0.923178\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −26.6247 | + | 26.6247i | −0.867939 | + | 0.867939i | −0.992244 | − | 0.124305i | \(-0.960330\pi\) |
0.124305 | + | 0.992244i | \(0.460330\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.07861i | 0.0676888i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 39.4502 | + | 39.4502i | 1.28196 | + | 1.28196i | 0.939552 | + | 0.342406i | \(0.111242\pi\) |
0.342406 | + | 0.939552i | \(0.388758\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −10.0579 | + | 10.0579i | −0.326493 | + | 0.326493i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −7.54083 | −0.244271 | −0.122136 | − | 0.992513i | \(-0.538974\pi\) | ||||
−0.122136 | + | 0.992513i | \(0.538974\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −50.6309 | − | 50.6309i | −1.63838 | − | 1.63838i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −8.84548 | −0.285635 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 23.9227 | 0.771698 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −37.1663 | − | 37.1663i | −1.19643 | − | 1.19643i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −19.3259 | −0.621480 | −0.310740 | − | 0.950495i | \(-0.600577\pi\) | ||||
−0.310740 | + | 0.950495i | \(0.600577\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −38.7441 | + | 38.7441i | −1.24336 | + | 1.24336i | −0.284760 | + | 0.958599i | \(0.591914\pi\) |
−0.958599 | + | 0.284760i | \(0.908086\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5.85221 | − | 5.85221i | −0.187613 | − | 0.187613i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 1.45784i | − | 0.0466404i | −0.999728 | − | 0.0233202i | \(-0.992576\pi\) | ||
0.999728 | − | 0.0233202i | \(-0.00742372\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.63580 | + | 2.63580i | −0.0842407 | + | 0.0842407i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 25.9206i | 0.826740i | 0.910563 | + | 0.413370i | \(0.135648\pi\) | ||||
−0.910563 | + | 0.413370i | \(0.864352\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 10.9789i | − | 0.349817i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.67664 | − | 4.67664i | 0.148708 | − | 0.148708i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 3.24733i | − | 0.103155i | −0.998669 | − | 0.0515775i | \(-0.983575\pi\) | ||
0.998669 | − | 0.0515775i | \(-0.0164249\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 22.0559 | + | 22.0559i | 0.699220 | + | 0.699220i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 16.0720 | − | 16.0720i | 0.509006 | − | 0.509006i | −0.405215 | − | 0.914221i | \(-0.632803\pi\) |
0.914221 | + | 0.405215i | \(0.132803\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 4032.2.v.d.1583.17 | 36 | ||
3.2 | odd | 2 | inner | 4032.2.v.d.1583.2 | 36 | ||
4.3 | odd | 2 | 1008.2.v.d.323.1 | ✓ | 36 | ||
12.11 | even | 2 | 1008.2.v.d.323.18 | yes | 36 | ||
16.5 | even | 4 | 1008.2.v.d.827.18 | yes | 36 | ||
16.11 | odd | 4 | inner | 4032.2.v.d.3599.2 | 36 | ||
48.5 | odd | 4 | 1008.2.v.d.827.1 | yes | 36 | ||
48.11 | even | 4 | inner | 4032.2.v.d.3599.17 | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1008.2.v.d.323.1 | ✓ | 36 | 4.3 | odd | 2 | ||
1008.2.v.d.323.18 | yes | 36 | 12.11 | even | 2 | ||
1008.2.v.d.827.1 | yes | 36 | 48.5 | odd | 4 | ||
1008.2.v.d.827.18 | yes | 36 | 16.5 | even | 4 | ||
4032.2.v.d.1583.2 | 36 | 3.2 | odd | 2 | inner | ||
4032.2.v.d.1583.17 | 36 | 1.1 | even | 1 | trivial | ||
4032.2.v.d.3599.2 | 36 | 16.11 | odd | 4 | inner | ||
4032.2.v.d.3599.17 | 36 | 48.11 | even | 4 | inner |