Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6012,2,Mod(3005,6012)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6012, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6012.3005");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6012 = 2^{2} \cdot 3^{2} \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6012.h (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: | \(48.0060616952\) |
Analytic rank: | \(0\) |
Dimension: | \(56\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3005.14 | ||
Character | \(\chi\) | \(=\) | 6012.3005 |
Dual form | 6012.2.h.a.3005.13 |
$q$-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 \(\left(\mathbb{Z}/6012\mathbb{Z}\right)^\times\).
\(n\) | \(3007\) | \(3341\) | \(4681\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.21423 | −0.990232 | −0.495116 | − | 0.868827i | \(-0.664874\pi\) | ||||
−0.495116 | + | 0.868827i | \(0.664874\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.10661 | −0.418260 | −0.209130 | − | 0.977888i | \(-0.567063\pi\) | ||||
−0.209130 | + | 0.977888i | \(0.567063\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 1.52623i | − | 0.460176i | −0.973170 | − | 0.230088i | \(-0.926099\pi\) | ||
0.973170 | − | 0.230088i | \(-0.0739015\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.26430i | 0.905354i | 0.891675 | + | 0.452677i | \(0.149531\pi\) | ||||
−0.891675 | + | 0.452677i | \(0.850469\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.68069 | −1.37777 | −0.688885 | − | 0.724870i | \(-0.741900\pi\) | ||||
−0.688885 | + | 0.724870i | \(0.741900\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.25231 | 1.43438 | 0.717189 | − | 0.696879i | \(-0.245428\pi\) | ||||
0.717189 | + | 0.696879i | \(0.245428\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.86296 | 1.01400 | 0.506998 | − | 0.861947i | \(-0.330755\pi\) | ||||
0.506998 | + | 0.861947i | \(0.330755\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.0972042 | −0.0194408 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 8.93164i | − | 1.65856i | −0.558830 | − | 0.829282i | \(-0.688750\pi\) | ||
0.558830 | − | 0.829282i | \(-0.311250\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.89423 | −0.340214 | −0.170107 | − | 0.985426i | \(-0.554411\pi\) | ||||
−0.170107 | + | 0.985426i | \(0.554411\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.45029 | 0.414174 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.41435i | 0.725714i | 0.931845 | + | 0.362857i | \(0.118199\pi\) | ||||
−0.931845 | + | 0.362857i | \(0.881801\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.75307 | −0.429957 | −0.214979 | − | 0.976619i | \(-0.568968\pi\) | ||||
−0.214979 | + | 0.976619i | \(0.568968\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.818459i | 0.124814i | 0.998051 | + | 0.0624069i | \(0.0198777\pi\) | ||||
−0.998051 | + | 0.0624069i | \(0.980122\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.00307i | 0.438042i | 0.975720 | + | 0.219021i | \(0.0702864\pi\) | ||||
−0.975720 | + | 0.219021i | \(0.929714\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.77541 | −0.825059 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9.36175 | −1.28594 | −0.642968 | − | 0.765893i | \(-0.722297\pi\) | ||||
−0.642968 | + | 0.765893i | \(0.722297\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.37942i | 0.455681i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.10719 | −0.534710 | −0.267355 | − | 0.963598i | \(-0.586150\pi\) | ||||
−0.267355 | + | 0.963598i | \(0.586150\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −12.1085 | −1.55033 | −0.775166 | − | 0.631757i | \(-0.782334\pi\) | ||||
−0.775166 | + | 0.631757i | \(0.782334\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 7.22790i | − | 0.896510i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 9.17056i | − | 1.12036i | −0.828370 | − | 0.560181i | \(-0.810732\pi\) | ||
0.828370 | − | 0.560181i | \(-0.189268\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.9769 | 1.30271 | 0.651357 | − | 0.758771i | \(-0.274200\pi\) | ||||
0.651357 | + | 0.758771i | \(0.274200\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 5.25379i | − | 0.614910i | −0.951563 | − | 0.307455i | \(-0.900523\pi\) | ||
0.951563 | − | 0.307455i | \(-0.0994773\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.68895i | 0.192473i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.5472i | 1.29916i | 0.760294 | + | 0.649579i | \(0.225055\pi\) | ||||
−0.760294 | + | 0.649579i | \(0.774945\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.75501 | 0.631694 | 0.315847 | − | 0.948810i | \(-0.397711\pi\) | ||||
0.315847 | + | 0.948810i | \(0.397711\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 12.5783 | 1.36431 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 8.72974i | − | 0.925350i | −0.886528 | − | 0.462675i | \(-0.846890\pi\) | ||
0.886528 | − | 0.462675i | \(-0.153110\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 3.61231i | − | 0.378673i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −13.8440 | −1.42037 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 16.1024 | 1.63495 | 0.817473 | − | 0.575966i | \(-0.195374\pi\) | ||||
0.817473 | + | 0.575966i | \(0.195374\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13.4647 | 1.33978 | 0.669892 | − | 0.742458i | \(-0.266340\pi\) | ||||
0.669892 | + | 0.742458i | \(0.266340\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.52408i | 0.938435i | 0.883083 | + | 0.469218i | \(0.155464\pi\) | ||||
−0.883083 | + | 0.469218i | \(0.844536\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 15.5883i | 1.50698i | 0.657459 | + | 0.753490i | \(0.271631\pi\) | ||||
−0.657459 | + | 0.753490i | \(0.728369\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 16.7828i | 1.60750i | 0.594969 | + | 0.803748i | \(0.297164\pi\) | ||||
−0.594969 | + | 0.803748i | \(0.702836\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.82248 | 0.359589 | 0.179794 | − | 0.983704i | \(-0.442457\pi\) | ||||
0.179794 | + | 0.983704i | \(0.442457\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −10.7677 | −1.00409 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.28632 | 0.576266 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.67061 | 0.788238 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.2864 | 1.00948 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 18.2667 | 1.62091 | 0.810454 | − | 0.585802i | \(-0.199220\pi\) | ||||
0.810454 | + | 0.585802i | \(0.199220\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.659035 | 0.0575801 | 0.0287901 | − | 0.999585i | \(-0.490835\pi\) | ||||
0.0287901 | + | 0.999585i | \(0.490835\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.91888 | −0.599943 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 4.04200i | − | 0.345331i | −0.984980 | − | 0.172666i | \(-0.944762\pi\) | ||
0.984980 | − | 0.172666i | \(-0.0552380\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 7.65339i | − | 0.649152i | −0.945860 | − | 0.324576i | \(-0.894778\pi\) | ||
0.945860 | − | 0.324576i | \(-0.105222\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.98208 | 0.416623 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 19.7767i | 1.64236i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 7.28994 | 0.597215 | 0.298608 | − | 0.954376i | \(-0.403478\pi\) | ||||
0.298608 | + | 0.954376i | \(0.403478\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.47956i | 0.283163i | 0.989927 | + | 0.141581i | \(0.0452187\pi\) | ||||
−0.989927 | + | 0.141581i | \(0.954781\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.19425 | 0.336890 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.65246 | 0.291498 | 0.145749 | − | 0.989322i | \(-0.453441\pi\) | ||||
0.145749 | + | 0.989322i | \(0.453441\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.38140 | −0.424114 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.688646i | 0.0539389i | 0.999636 | + | 0.0269695i | \(0.00858569\pi\) | ||||
−0.999636 | + | 0.0269695i | \(0.991414\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −8.71933 | − | 9.53799i | −0.674722 | − | 0.738072i | ||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.34434 | 0.180334 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 22.9194i | − | 1.74253i | −0.490817 | − | 0.871263i | \(-0.663301\pi\) | ||
0.490817 | − | 0.871263i | \(-0.336699\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.107567 | 0.00813132 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 12.0216i | − | 0.898538i | −0.893396 | − | 0.449269i | \(-0.851684\pi\) | ||
0.893396 | − | 0.449269i | \(-0.148316\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.52740 | 0.262190 | 0.131095 | − | 0.991370i | \(-0.458151\pi\) | ||||
0.131095 | + | 0.991370i | \(0.458151\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 9.77436i | − | 0.718625i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.67006i | 0.634018i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 12.9390i | − | 0.936233i | −0.883667 | − | 0.468116i | \(-0.844933\pi\) | ||
0.883667 | − | 0.468116i | \(-0.155067\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.2433i | 0.737327i | 0.929563 | + | 0.368664i | \(0.120185\pi\) | ||||
−0.929563 | + | 0.368664i | \(0.879815\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 18.8008 | 1.33950 | 0.669750 | − | 0.742587i | \(-0.266401\pi\) | ||||
0.669750 | + | 0.742587i | \(0.266401\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 15.3128 | 1.08549 | 0.542747 | − | 0.839896i | \(-0.317384\pi\) | ||||
0.542747 | + | 0.839896i | \(0.317384\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 9.88386i | 0.693711i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.09592 | 0.425757 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 9.54248i | − | 0.660067i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.41188 | 0.372569 | 0.186285 | − | 0.982496i | \(-0.440355\pi\) | ||||
0.186285 | + | 0.982496i | \(0.440355\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 1.81225i | − | 0.123595i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.09618 | 0.142298 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 18.5435i | − | 1.24737i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 20.0075 | 1.33980 | 0.669902 | − | 0.742450i | \(-0.266336\pi\) | ||||
0.669902 | + | 0.742450i | \(0.266336\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 15.2335 | 1.01108 | 0.505541 | − | 0.862802i | \(-0.331293\pi\) | ||||
0.505541 | + | 0.862802i | \(0.331293\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.19317 | 0.343175 | 0.171587 | − | 0.985169i | \(-0.445110\pi\) | ||||
0.171587 | + | 0.985169i | \(0.445110\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 17.8919i | 1.17213i | 0.810262 | + | 0.586067i | \(0.199325\pi\) | ||||
−0.810262 | + | 0.586067i | \(0.800675\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 6.64947i | − | 0.433763i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 9.92922i | 0.642268i | 0.947034 | + | 0.321134i | \(0.104064\pi\) | ||||
−0.947034 | + | 0.321134i | \(0.895936\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.09323i | 0.0704210i | 0.999380 | + | 0.0352105i | \(0.0112102\pi\) | ||||
−0.999380 | + | 0.0352105i | \(0.988790\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 12.7881 | 0.816999 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 20.4094i | 1.29862i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 12.1099i | 0.764368i | 0.924086 | + | 0.382184i | \(0.124828\pi\) | ||||
−0.924086 | + | 0.382184i | \(0.875172\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 7.42200i | − | 0.466617i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.89139 | 0.117982 | 0.0589908 | − | 0.998259i | \(-0.481212\pi\) | ||||
0.0589908 | + | 0.998259i | \(0.481212\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 4.88497i | − | 0.303537i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 0.0895652i | − | 0.00552282i | −0.999996 | − | 0.00276141i | \(-0.999121\pi\) | ||
0.999996 | − | 0.00276141i | \(-0.000878986\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 20.7290 | 1.27337 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −25.1217 | −1.53170 | −0.765849 | − | 0.643020i | \(-0.777681\pi\) | ||||
−0.765849 | + | 0.643020i | \(0.777681\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 32.9056i | − | 1.99887i | −0.0335917 | − | 0.999436i | \(-0.510695\pi\) | ||
0.0335917 | − | 0.999436i | \(-0.489305\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.148356i | 0.00894621i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.38325i | 0.203280i | 0.994821 | + | 0.101640i | \(0.0324090\pi\) | ||||
−0.994821 | + | 0.101640i | \(0.967591\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 16.9847i | 1.01322i | 0.862175 | + | 0.506611i | \(0.169102\pi\) | ||||
−0.862175 | + | 0.506611i | \(0.830898\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −15.2318 | −0.905436 | −0.452718 | − | 0.891654i | \(-0.649546\pi\) | ||||
−0.452718 | + | 0.891654i | \(0.649546\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.04658 | 0.179834 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 15.2703 | 0.898252 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5.64421i | 0.329738i | 0.986315 | + | 0.164869i | \(0.0527202\pi\) | ||||
−0.986315 | + | 0.164869i | \(0.947280\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9.09424 | 0.529487 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 15.8742i | 0.918026i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 0.905717i | − | 0.0522046i | ||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 26.8109 | 1.53519 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 23.8883i | 1.36338i | 0.731643 | + | 0.681688i | \(0.238754\pi\) | ||||
−0.731643 | + | 0.681688i | \(0.761246\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 14.1909i | − | 0.804690i | −0.915488 | − | 0.402345i | \(-0.868195\pi\) | ||
0.915488 | − | 0.402345i | \(-0.131805\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.69765i | 0.548143i | 0.961709 | + | 0.274072i | \(0.0883706\pi\) | ||||
−0.961709 | + | 0.274072i | \(0.911629\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 8.30637i | − | 0.466532i | −0.972413 | − | 0.233266i | \(-0.925059\pi\) | ||
0.972413 | − | 0.233266i | \(-0.0749413\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −13.6318 | −0.763232 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −35.5175 | −1.97624 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 0.317304i | − | 0.0176008i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 3.32323i | − | 0.183216i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 14.1080i | − | 0.775447i | −0.921776 | − | 0.387723i | \(-0.873262\pi\) | ||
0.921776 | − | 0.387723i | \(-0.126738\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 20.3057i | 1.10942i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 29.0529 | 1.58261 | 0.791307 | − | 0.611419i | \(-0.209401\pi\) | ||||
0.791307 | + | 0.611419i | \(0.209401\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.89103i | 0.156558i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 14.1374 | 0.763349 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 16.1997 | 0.869645 | 0.434822 | − | 0.900516i | \(-0.356811\pi\) | ||||
0.434822 | + | 0.900516i | \(0.356811\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 16.0230i | 0.857694i | 0.903377 | + | 0.428847i | \(0.141080\pi\) | ||||
−0.903377 | + | 0.428847i | \(0.858920\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 11.7462i | 0.625185i | 0.949887 | + | 0.312593i | \(0.101197\pi\) | ||||
−0.949887 | + | 0.312593i | \(0.898803\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −24.3053 | −1.28999 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 9.78407i | 0.516383i | 0.966094 | + | 0.258192i | \(0.0831266\pi\) | ||||
−0.966094 | + | 0.258192i | \(0.916873\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 20.0914 | 1.05744 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 11.6331i | 0.608903i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.46441 | 0.441838 | 0.220919 | − | 0.975292i | \(-0.429094\pi\) | ||||
0.220919 | + | 0.975292i | \(0.429094\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 10.3598 | 0.537855 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 36.5181i | 1.89084i | 0.325859 | + | 0.945418i | \(0.394346\pi\) | ||||
−0.325859 | + | 0.945418i | \(0.605654\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 29.1556 | 1.50159 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 35.7780i | − | 1.83779i | −0.394497 | − | 0.918897i | \(-0.629081\pi\) | ||
0.394497 | − | 0.918897i | \(-0.370919\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 31.2989i | − | 1.59930i | −0.600465 | − | 0.799651i | \(-0.705018\pi\) | ||
0.600465 | − | 0.799651i | \(-0.294982\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − | 3.73971i | − | 0.190593i | ||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 35.3084 | 1.79021 | 0.895104 | − | 0.445857i | \(-0.147101\pi\) | ||||
0.895104 | + | 0.445857i | \(0.147101\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −27.6250 | −1.39705 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 25.5680i | − | 1.28647i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 16.7323 | 0.839773 | 0.419886 | − | 0.907577i | \(-0.362070\pi\) | ||||
0.419886 | + | 0.907577i | \(0.362070\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −17.1969 | −0.858772 | −0.429386 | − | 0.903121i | \(-0.641270\pi\) | ||||
−0.429386 | + | 0.903121i | \(0.641270\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 6.18333i | − | 0.308014i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.73732 | 0.333957 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −16.6768 | −0.824614 | −0.412307 | − | 0.911045i | \(-0.635277\pi\) | ||||
−0.412307 | + | 0.911045i | \(0.635277\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.54506 | 0.223648 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −12.7429 | −0.625523 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.19272i | 0.253681i | 0.991923 | + | 0.126841i | \(0.0404836\pi\) | ||||
−0.991923 | + | 0.126841i | \(0.959516\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 38.6414 | 1.88327 | 0.941633 | − | 0.336641i | \(-0.109291\pi\) | ||||
0.941633 | + | 0.336641i | \(0.109291\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.552187 | 0.0267850 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 13.3994 | 0.648442 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 29.8086i | 1.43583i | 0.696130 | + | 0.717916i | \(0.254904\pi\) | ||||
−0.696130 | + | 0.717916i | \(0.745096\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −23.5768 | −1.13303 | −0.566515 | − | 0.824052i | \(-0.691709\pi\) | ||||
−0.566515 | + | 0.824052i | \(0.691709\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 30.4047 | 1.45445 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 33.7776i | − | 1.61212i | −0.591836 | − | 0.806058i | \(-0.701597\pi\) | ||
0.591836 | − | 0.806058i | \(-0.298403\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5.82132 | 0.276579 | 0.138290 | − | 0.990392i | \(-0.455839\pi\) | ||||
0.138290 | + | 0.990392i | \(0.455839\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 19.3296i | 0.916311i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 31.1572i | − | 1.47040i | −0.677850 | − | 0.735201i | \(-0.737088\pi\) | ||
0.677850 | − | 0.735201i | \(-0.262912\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.20183i | 0.197856i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 7.99848i | 0.374974i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9.38086i | 0.438818i | 0.975633 | + | 0.219409i | \(0.0704129\pi\) | ||||
−0.975633 | + | 0.219409i | \(0.929587\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 42.4425i | − | 1.97674i | −0.152053 | − | 0.988372i | \(-0.548588\pi\) | ||
0.152053 | − | 0.988372i | \(-0.451412\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9.06979i | 0.421509i | 0.977539 | + | 0.210754i | \(0.0675921\pi\) | ||||
−0.977539 | + | 0.210754i | \(0.932408\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 4.77793i | − | 0.221096i | −0.993871 | − | 0.110548i | \(-0.964739\pi\) | ||
0.993871 | − | 0.110548i | \(-0.0352606\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 10.1482i | 0.468603i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.24916 | 0.0574364 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.607750 | −0.0278855 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −0.0102115 | −0.000466577 | −0.000233289 | − | 1.00000i | \(-0.500074\pi\) | ||||
−0.000233289 | 1.00000i | \(0.500074\pi\) | ||||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −14.4098 | −0.657028 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −35.6543 | −1.61898 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 33.4280i | 1.51477i | 0.652971 | + | 0.757383i | \(0.273522\pi\) | ||||
−0.652971 | + | 0.757383i | \(0.726478\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 22.1905i | 1.00144i | 0.865608 | + | 0.500722i | \(0.166932\pi\) | ||||
−0.865608 | + | 0.500722i | \(0.833068\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 50.7379i | 2.28512i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −12.1471 | −0.544873 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 41.2840i | 1.84813i | 0.382238 | + | 0.924064i | \(0.375153\pi\) | ||||
−0.382238 | + | 0.924064i | \(0.624847\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 32.2498i | − | 1.43795i | −0.695037 | − | 0.718974i | \(-0.744612\pi\) | ||
0.695037 | − | 0.718974i | \(-0.255388\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −29.8138 | −1.32670 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 15.7838i | 0.699603i | 0.936824 | + | 0.349802i | \(0.113751\pi\) | ||||
−0.936824 | + | 0.349802i | \(0.886249\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.81391i | 0.257192i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 21.0885i | − | 0.929269i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.58338 | 0.201577 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −38.8058 | −1.70011 | −0.850057 | − | 0.526691i | \(-0.823432\pi\) | ||||
−0.850057 | + | 0.526691i | \(0.823432\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 19.8033 | 0.865940 | 0.432970 | − | 0.901408i | \(-0.357466\pi\) | ||||
0.432970 | + | 0.901408i | \(0.357466\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 10.7605 | 0.468736 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.648346 | 0.0281890 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 8.98685i | − | 0.389264i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 34.5161i | − | 1.49226i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 8.81462i | 0.379673i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 29.3779i | − | 1.26305i | −0.775354 | − | 0.631527i | \(-0.782429\pi\) | ||
0.775354 | − | 0.631527i | \(-0.217571\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 37.1608i | − | 1.59179i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 43.1267i | − | 1.84397i | −0.387231 | − | 0.921983i | \(-0.626568\pi\) | ||
0.387231 | − | 0.921983i | \(-0.373432\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 55.8434i | − | 2.37901i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 12.7782i | − | 0.543386i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 39.1934i | 1.66068i | 0.557259 | + | 0.830339i | \(0.311853\pi\) | ||||
−0.557259 | + | 0.830339i | \(0.688147\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.67170 | −0.113001 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 32.6676i | − | 1.37678i | −0.725342 | − | 0.688388i | \(-0.758319\pi\) | ||
0.725342 | − | 0.688388i | \(-0.241681\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8.46384 | −0.356076 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −27.4263 | −1.14977 | −0.574885 | − | 0.818234i | \(-0.694953\pi\) | ||||
−0.574885 | + | 0.818234i | \(0.694953\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.53874i | 0.399184i | 0.979879 | + | 0.199592i | \(0.0639616\pi\) | ||||
−0.979879 | + | 0.199592i | \(0.936038\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.472700 | −0.0197129 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8.45388 | −0.351940 | −0.175970 | − | 0.984396i | \(-0.556306\pi\) | ||||
−0.175970 | + | 0.984396i | \(0.556306\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.36856 | −0.264212 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 14.2882i | 0.591757i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −16.7100 | −0.689696 | −0.344848 | − | 0.938659i | \(-0.612070\pi\) | ||||
−0.344848 | + | 0.938659i | \(0.612070\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −11.8433 | −0.487995 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 5.86014 | 0.240647 | 0.120324 | − | 0.992735i | \(-0.461607\pi\) | ||||
0.120324 | + | 0.992735i | \(0.461607\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −13.9193 | −0.570637 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 46.3364i | 1.89326i | 0.322329 | + | 0.946628i | \(0.395534\pi\) | ||||
−0.322329 | + | 0.946628i | \(0.604466\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 14.8468 | 0.605615 | 0.302807 | − | 0.953052i | \(-0.402076\pi\) | ||||
0.302807 | + | 0.953052i | \(0.402076\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −19.1987 | −0.780538 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 16.2655i | 0.660196i | 0.943947 | + | 0.330098i | \(0.107082\pi\) | ||||
−0.943947 | + | 0.330098i | \(0.892918\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −9.80291 | −0.396583 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.116515 | 0.00470602 | 0.00235301 | − | 0.999997i | \(-0.499251\pi\) | ||||
0.00235301 | + | 0.999997i | \(0.499251\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.36390i | 0.0549084i | 0.999623 | + | 0.0274542i | \(0.00874004\pi\) | ||||
−0.999623 | + | 0.0274542i | \(0.991260\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 18.6289i | 0.748759i | 0.927276 | + | 0.374379i | \(0.122144\pi\) | ||||
−0.927276 | + | 0.374379i | \(0.877856\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 9.66043i | 0.387037i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −24.5045 | −0.980181 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 25.0766i | − | 0.999868i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.81751 | 0.351019 | 0.175510 | − | 0.984478i | \(-0.443843\pi\) | ||||
0.175510 | + | 0.984478i | \(0.443843\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −40.4466 | −1.60508 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 18.8527i | − | 0.746970i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 14.4116 | 0.569224 | 0.284612 | − | 0.958643i | \(-0.408135\pi\) | ||||
0.284612 | + | 0.958643i | \(0.408135\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 36.3292i | 1.43268i | 0.697749 | + | 0.716342i | \(0.254185\pi\) | ||||
−0.697749 | + | 0.716342i | \(0.745815\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 13.6166 | 0.535322 | 0.267661 | − | 0.963513i | \(-0.413749\pi\) | ||||
0.267661 | + | 0.963513i | \(0.413749\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.26853i | 0.246061i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 22.5752i | 0.883437i | 0.897154 | + | 0.441718i | \(0.145631\pi\) | ||||
−0.897154 | + | 0.441718i | \(0.854369\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.45925 | −0.0570177 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.04987 | 0.0798518 | 0.0399259 | − | 0.999203i | \(-0.487288\pi\) | ||||
0.0399259 | + | 0.999203i | \(0.487288\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 24.1084i | 0.937708i | 0.883276 | + | 0.468854i | \(0.155333\pi\) | ||||
−0.883276 | + | 0.468854i | \(0.844667\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 15.3200 | 0.594082 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 43.4342i | − | 1.68178i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 18.4804i | 0.713426i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.80060i | 0.223597i | 0.993731 | + | 0.111798i | \(0.0356611\pi\) | ||||
−0.993731 | + | 0.111798i | \(0.964339\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 1.60083i | − | 0.0615248i | −0.999527 | − | 0.0307624i | \(-0.990206\pi\) | ||
0.999527 | − | 0.0307624i | \(-0.00979352\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −17.8191 | −0.683833 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 26.7110 | 1.02207 | 0.511034 | − | 0.859560i | \(-0.329263\pi\) | ||||
0.511034 | + | 0.859560i | \(0.329263\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.94990i | 0.341958i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 30.5596i | − | 1.16423i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 14.0321i | − | 0.533808i | −0.963723 | − | 0.266904i | \(-0.913999\pi\) | ||
0.963723 | − | 0.266904i | \(-0.0860006\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 16.9463i | 0.642811i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 15.6393 | 0.592382 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 50.1976i | 1.89594i | 0.318364 | + | 0.947969i | \(0.396867\pi\) | ||||
−0.318364 | + | 0.947969i | \(0.603133\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 27.5999i | 1.04095i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −14.9002 | −0.560378 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 23.4320i | − | 0.880009i | −0.897996 | − | 0.440004i | \(-0.854977\pi\) | ||
0.897996 | − | 0.440004i | \(-0.145023\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −9.21155 | −0.344975 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −11.0315 | −0.412553 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −36.5966 | −1.36482 | −0.682411 | − | 0.730969i | \(-0.739069\pi\) | ||||
−0.682411 | + | 0.730969i | \(0.739069\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 10.5395i | − | 0.392510i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.868193i | 0.0322439i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 24.8889i | − | 0.923080i | −0.887119 | − | 0.461540i | \(-0.847297\pi\) | ||
0.887119 | − | 0.461540i | \(-0.152703\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 4.64942i | − | 0.171965i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 11.4373 | 0.422446 | 0.211223 | − | 0.977438i | \(-0.432255\pi\) | ||||
0.211223 | + | 0.977438i | \(0.432255\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −13.9964 | −0.515564 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 36.0468i | − | 1.32600i | −0.748618 | − | 0.663001i | \(-0.769282\pi\) | ||
0.748618 | − | 0.663001i | \(-0.230718\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 12.2477i | 0.449324i | 0.974437 | + | 0.224662i | \(0.0721277\pi\) | ||||
−0.974437 | + | 0.224662i | \(0.927872\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −16.1416 | −0.591382 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 17.2502i | − | 0.630310i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.39744i | 0.306427i | 0.988193 | + | 0.153213i | \(0.0489622\pi\) | ||||
−0.988193 | + | 0.153213i | \(0.951038\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 7.70453i | − | 0.280397i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 39.7794 | 1.44581 | 0.722904 | − | 0.690949i | \(-0.242807\pi\) | ||||
0.722904 | + | 0.690949i | \(0.242807\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 16.9492i | 0.614409i | 0.951644 | + | 0.307205i | \(0.0993936\pi\) | ||||
−0.951644 | + | 0.307205i | \(0.900606\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 18.5720i | − | 0.672351i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 13.4071i | − | 0.484102i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 0.808888i | − | 0.0291692i | −0.999894 | − | 0.0145846i | \(-0.995357\pi\) | ||
0.999894 | − | 0.0145846i | \(-0.00464259\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 21.1557 | 0.760919 | 0.380459 | − | 0.924798i | \(-0.375766\pi\) | ||||
0.380459 | + | 0.924798i | \(0.375766\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.184127 | 0.00661404 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −17.2130 | −0.616721 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 16.7533i | − | 0.599479i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −8.08738 | −0.288651 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 20.5075i | − | 0.731015i | −0.930808 | − | 0.365508i | \(-0.880895\pi\) | ||
0.930808 | − | 0.365508i | \(-0.119105\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.23000 | −0.150402 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 39.5257i | − | 1.40360i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.49394 | 0.0883398 | 0.0441699 | − | 0.999024i | \(-0.485936\pi\) | ||||
0.0441699 | + | 0.999024i | \(0.485936\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 17.0595i | − | 0.603522i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −8.01851 | −0.282967 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 11.9156 | 0.419971 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 45.2751i | − | 1.59179i | −0.605437 | − | 0.795893i | \(-0.707002\pi\) | ||
0.605437 | − | 0.795893i | \(-0.292998\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 29.4613i | 1.03453i | 0.855826 | + | 0.517264i | \(0.173049\pi\) | ||||
−0.855826 | + | 0.517264i | \(0.826951\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 1.52482i | − | 0.0534120i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.11726i | 0.179030i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 32.1577 | 1.12231 | 0.561157 | − | 0.827710i | \(-0.310357\pi\) | ||||
0.561157 | + | 0.827710i | \(0.310357\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 12.4505i | − | 0.433997i | −0.976172 | − | 0.216998i | \(-0.930373\pi\) | ||
0.976172 | − | 0.216998i | \(-0.0696267\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 45.4844 | 1.58165 | 0.790824 | − | 0.612043i | \(-0.209652\pi\) | ||||
0.790824 | + | 0.612043i | \(0.209652\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 26.3397i | − | 0.914814i | −0.889257 | − | 0.457407i | \(-0.848778\pi\) | ||
0.889257 | − | 0.457407i | \(-0.151222\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 32.8083 | 1.13674 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 19.3066 | + | 21.1193i | 0.668132 | + | 0.730862i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 7.89720i | 0.272642i | 0.990665 | + | 0.136321i | \(0.0435278\pi\) | ||||
−0.990665 | + | 0.136321i | \(0.956472\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −50.7742 | −1.75083 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −5.19090 | −0.178572 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −9.59500 | −0.329688 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 21.4668i | 0.735872i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 24.0348 | 0.822936 | 0.411468 | − | 0.911424i | \(-0.365016\pi\) | ||||
0.411468 | + | 0.911424i | \(0.365016\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 21.7787i | − | 0.743945i | −0.928244 | − | 0.371973i | \(-0.878682\pi\) | ||
0.928244 | − | 0.371973i | \(-0.121318\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −9.15430 | −0.312341 | −0.156170 | − | 0.987730i | \(-0.549915\pi\) | ||||
−0.156170 | + | 0.987730i | \(0.549915\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0.493931i | 0.0168136i | 0.999965 | + | 0.00840681i | \(0.00267600\pi\) | ||||
−0.999965 | + | 0.00840681i | \(0.997324\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 50.7486i | 1.72550i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 17.6237 | 0.597842 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 29.9355 | 1.01432 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −12.4896 | −0.422226 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.67415 | 0.0902995 | 0.0451498 | − | 0.998980i | \(-0.485623\pi\) | ||||
0.0451498 | + | 0.998980i | \(0.485623\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 9.60269 | 0.323523 | 0.161761 | − | 0.986830i | \(-0.448282\pi\) | ||||
0.161761 | + | 0.986830i | \(0.448282\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −21.8319 | −0.734702 | −0.367351 | − | 0.930082i | \(-0.619735\pi\) | ||||
−0.367351 | + | 0.930082i | \(0.619735\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −15.7780 | −0.529774 | −0.264887 | − | 0.964279i | \(-0.585335\pi\) | ||||
−0.264887 | + | 0.964279i | \(0.585335\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −20.2142 | −0.677961 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 18.7761i | 0.628318i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 26.6186i | 0.889761i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 16.9186i | 0.564266i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 53.1812 | 1.77172 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −7.81047 | −0.259629 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 35.1728 | 1.16789 | 0.583947 | − | 0.811792i | \(-0.301508\pi\) | ||||
0.583947 | + | 0.811792i | \(0.301508\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 54.7431i | 1.81372i | 0.421432 | + | 0.906860i | \(0.361528\pi\) | ||||
−0.421432 | + | 0.906860i | \(0.638472\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 8.78348i | − | 0.290691i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −0.729295 | −0.0240835 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −47.4360 | −1.56477 | −0.782384 | − | 0.622796i | \(-0.785997\pi\) | ||||
−0.782384 | + | 0.622796i | \(0.785997\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 35.8318i | 1.17942i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 0.429093i | − | 0.0141085i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 20.8057i | 0.682612i | 0.939952 | + | 0.341306i | \(0.110869\pi\) | ||||
−0.939952 | + | 0.341306i | \(0.889131\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −36.1097 | −1.18345 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 19.1975i | − | 0.627825i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.84765i | 0.125697i | 0.998023 | + | 0.0628486i | \(0.0200185\pi\) | ||||
−0.998023 | + | 0.0628486i | \(0.979981\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 25.7928 | 0.840821 | 0.420411 | − | 0.907334i | \(-0.361886\pi\) | ||||
0.420411 | + | 0.907334i | \(0.361886\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −13.3881 | −0.435975 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 13.5461i | 0.440189i | 0.975479 | + | 0.220094i | \(0.0706365\pi\) | ||||
−0.975479 | + | 0.220094i | \(0.929363\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 17.1500 | 0.556711 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −43.3539 | −1.40437 | −0.702185 | − | 0.711994i | \(-0.747792\pi\) | ||||
−0.702185 | + | 0.711994i | \(0.747792\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 28.6499i | 0.927088i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4.47292i | 0.144438i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.4119 | −0.884255 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 22.6809i | − | 0.730125i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −36.1147 | −1.16137 | −0.580686 | − | 0.814128i | \(-0.697215\pi\) | ||||
−0.580686 | + | 0.814128i | \(0.697215\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 36.5547 | 1.17310 | 0.586549 | − | 0.809914i | \(-0.300486\pi\) | ||||
0.586549 | + | 0.809914i | \(0.300486\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8.46933i | 0.271514i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −21.0142 | −0.672304 | −0.336152 | − | 0.941808i | \(-0.609126\pi\) | ||||
−0.336152 | + | 0.941808i | \(0.609126\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −13.3236 | −0.425824 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −5.90153 | −0.188230 | −0.0941149 | − | 0.995561i | \(-0.530002\pi\) | ||||
−0.0941149 | + | 0.995561i | \(0.530002\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −41.6292 | −1.32642 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.98013i | 0.126561i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 41.3636i | − | 1.31396i | −0.753909 | − | 0.656979i | \(-0.771834\pi\) | ||
0.753909 | − | 0.656979i | \(-0.228166\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −33.9059 | −1.07489 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −25.2647 | −0.800140 | −0.400070 | − | 0.916485i | \(-0.631014\pi\) | ||||
−0.400070 | + | 0.916485i | \(0.631014\pi\) | |||||||
\(998\) | 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 | 6012.2.h.a.3005.14 | yes | 56 | |
3.2 | odd | 2 | inner | 6012.2.h.a.3005.44 | yes | 56 | |
167.166 | odd | 2 | inner | 6012.2.h.a.3005.43 | yes | 56 | |
501.500 | even | 2 | inner | 6012.2.h.a.3005.13 | ✓ | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6012.2.h.a.3005.13 | ✓ | 56 | 501.500 | even | 2 | inner | |
6012.2.h.a.3005.14 | yes | 56 | 1.1 | even | 1 | trivial | |
6012.2.h.a.3005.43 | yes | 56 | 167.166 | odd | 2 | inner | |
6012.2.h.a.3005.44 | yes | 56 | 3.2 | odd | 2 | inner |