Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1400,2,Mod(657,1400)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1400, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 0, 1, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1400.657");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1400 = 2^{3} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1400.x (of order \(4\), degree \(2\), 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: | \(11.1790562830\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 993.7 | ||
Character | \(\chi\) | \(=\) | 1400.993 |
Dual form | 1400.2.x.c.657.7 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1400\mathbb{Z}\right)^\times\).
\(n\) | \(351\) | \(701\) | \(801\) | \(1177\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
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 | ||||||||
\(3\) | −0.409160 | + | 0.409160i | −0.236229 | + | 0.236229i | −0.815287 | − | 0.579058i | \(-0.803421\pi\) |
0.579058 | + | 0.815287i | \(0.303421\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.738062 | + | 2.54072i | 0.278961 | + | 0.960302i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.66518i | 0.888392i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.54935 | −1.07017 | −0.535084 | − | 0.844799i | \(-0.679720\pi\) | ||||
−0.535084 | + | 0.844799i | \(0.679720\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.95189 | + | 2.95189i | −0.818708 | + | 0.818708i | −0.985921 | − | 0.167213i | \(-0.946523\pi\) |
0.167213 | + | 0.985921i | \(0.446523\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.59675 | − | 5.59675i | −1.35741 | − | 1.35741i | −0.877097 | − | 0.480314i | \(-0.840523\pi\) |
−0.480314 | − | 0.877097i | \(-0.659477\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.59597 | 0.824972 | 0.412486 | − | 0.910964i | \(-0.364661\pi\) | ||||
0.412486 | + | 0.910964i | \(0.364661\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.34155 | − | 0.737576i | −0.292750 | − | 0.160952i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.0472877 | − | 0.0472877i | −0.00986016 | − | 0.00986016i | 0.702160 | − | 0.712020i | \(-0.252219\pi\) |
−0.712020 | + | 0.702160i | \(0.752219\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.31796 | − | 2.31796i | −0.446092 | − | 0.446092i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 5.34827i | − | 0.993149i | −0.867994 | − | 0.496574i | \(-0.834591\pi\) | ||
0.867994 | − | 0.496574i | \(-0.165409\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 10.3924i | − | 1.86653i | −0.359192 | − | 0.933264i | \(-0.616948\pi\) | ||
0.359192 | − | 0.933264i | \(-0.383052\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.45225 | − | 1.45225i | 0.252804 | − | 0.252804i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.80067 | + | 7.80067i | −1.28242 | + | 1.28242i | −0.343137 | + | 0.939285i | \(0.611490\pi\) |
−0.939285 | + | 0.343137i | \(0.888510\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 2.41560i | − | 0.386805i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 5.63913i | − | 0.880685i | −0.897830 | − | 0.440342i | \(-0.854857\pi\) | ||
0.897830 | − | 0.440342i | \(-0.145143\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.93871 | + | 6.93871i | 1.05814 | + | 1.05814i | 0.998202 | + | 0.0599420i | \(0.0190916\pi\) |
0.0599420 | + | 0.998202i | \(0.480908\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.44333 | − | 3.44333i | −0.502261 | − | 0.502261i | 0.409879 | − | 0.912140i | \(-0.365571\pi\) |
−0.912140 | + | 0.409879i | \(0.865571\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.91053 | + | 3.75042i | −0.844361 | + | 0.535774i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.57993 | 0.641319 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.646830 | − | 0.646830i | −0.0888490 | − | 0.0888490i | 0.661285 | − | 0.750134i | \(-0.270011\pi\) |
−0.750134 | + | 0.661285i | \(0.770011\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.47133 | + | 1.47133i | −0.194882 | + | 0.194882i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.22732 | 1.20130 | 0.600648 | − | 0.799514i | \(-0.294910\pi\) | ||||
0.600648 | + | 0.799514i | \(0.294910\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 3.51832i | − | 0.450474i | −0.974304 | − | 0.225237i | \(-0.927684\pi\) | ||
0.974304 | − | 0.225237i | \(-0.0723157\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −6.77147 | + | 1.96707i | −0.853125 | + | 0.247827i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.70777 | − | 1.70777i | 0.208637 | − | 0.208637i | −0.595051 | − | 0.803688i | \(-0.702868\pi\) |
0.803688 | + | 0.595051i | \(0.202868\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.0386965 | 0.00465851 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.54487 | −1.01409 | −0.507045 | − | 0.861920i | \(-0.669262\pi\) | ||||
−0.507045 | + | 0.861920i | \(0.669262\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.43511 | + | 2.43511i | −0.285009 | + | 0.285009i | −0.835103 | − | 0.550094i | \(-0.814592\pi\) |
0.550094 | + | 0.835103i | \(0.314592\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.61964 | − | 9.01790i | −0.298535 | − | 1.02768i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.72713i | 0.644352i | 0.946680 | + | 0.322176i | \(0.104414\pi\) | ||||
−0.946680 | + | 0.322176i | \(0.895586\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −6.09869 | −0.677632 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.04580 | + | 2.04580i | −0.224556 | + | 0.224556i | −0.810414 | − | 0.585858i | \(-0.800758\pi\) |
0.585858 | + | 0.810414i | \(0.300758\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.18830 | + | 2.18830i | 0.234610 | + | 0.234610i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −8.18639 | −0.867756 | −0.433878 | − | 0.900972i | \(-0.642855\pi\) | ||||
−0.433878 | + | 0.900972i | \(0.642855\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −9.67862 | − | 5.32126i | −1.01460 | − | 0.557820i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.25215 | + | 4.25215i | 0.440927 | + | 0.440927i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.23068 | − | 6.23068i | −0.632629 | − | 0.632629i | 0.316097 | − | 0.948727i | \(-0.397627\pi\) |
−0.948727 | + | 0.316097i | \(0.897627\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 9.45963i | − | 0.950729i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13.7868i | 1.37184i | 0.727677 | + | 0.685920i | \(0.240600\pi\) | ||||
−0.727677 | + | 0.685920i | \(0.759400\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.3752 | + | 10.3752i | −1.02230 | + | 1.02230i | −0.0225506 | + | 0.999746i | \(0.507179\pi\) |
−0.999746 | + | 0.0225506i | \(0.992821\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.54863 | + | 4.54863i | −0.439733 | + | 0.439733i | −0.891922 | − | 0.452189i | \(-0.850643\pi\) |
0.452189 | + | 0.891922i | \(0.350643\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.76387i | 0.360513i | 0.983620 | + | 0.180257i | \(0.0576928\pi\) | ||||
−0.983620 | + | 0.180257i | \(0.942307\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 6.38345i | − | 0.605890i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.83006 | − | 4.83006i | −0.454374 | − | 0.454374i | 0.442429 | − | 0.896803i | \(-0.354117\pi\) |
−0.896803 | + | 0.442429i | \(0.854117\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −7.86732 | − | 7.86732i | −0.727334 | − | 0.727334i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 10.0890 | − | 18.3505i | 0.924860 | − | 1.68219i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.59785 | 0.145259 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.30731 | + | 2.30731i | 0.208043 | + | 0.208043i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.86172 | − | 9.86172i | 0.875086 | − | 0.875086i | −0.117936 | − | 0.993021i | \(-0.537628\pi\) |
0.993021 | + | 0.117936i | \(0.0376276\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −5.67809 | −0.499928 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 13.8255i | − | 1.20794i | −0.797006 | − | 0.603971i | \(-0.793584\pi\) | ||
0.797006 | − | 0.603971i | \(-0.206416\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.65405 | + | 9.13636i | 0.230135 | + | 0.792223i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −13.2776 | + | 13.2776i | −1.13438 | + | 1.13438i | −0.144938 | + | 0.989441i | \(0.546298\pi\) |
−0.989441 | + | 0.144938i | \(0.953702\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.55843 | 0.641097 | 0.320549 | − | 0.947232i | \(-0.396133\pi\) | ||||
0.320549 | + | 0.947232i | \(0.396133\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.81774 | 0.237297 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 10.4773 | − | 10.4773i | 0.876155 | − | 0.876155i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.883831 | − | 3.95288i | 0.0728971 | − | 0.326028i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 17.1912i | 1.40836i | 0.710021 | + | 0.704180i | \(0.248685\pi\) | ||||
−0.710021 | + | 0.704180i | \(0.751315\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.81237 | 0.554383 | 0.277192 | − | 0.960815i | \(-0.410596\pi\) | ||||
0.277192 | + | 0.960815i | \(0.410596\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 14.9163 | − | 14.9163i | 1.20591 | − | 1.20591i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.15071 | − | 1.15071i | −0.0918367 | − | 0.0918367i | 0.659696 | − | 0.751533i | \(-0.270685\pi\) |
−0.751533 | + | 0.659696i | \(0.770685\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.529315 | 0.0419774 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.0852436 | − | 0.155046i | 0.00671814 | − | 0.0122193i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −10.4137 | − | 10.4137i | −0.815660 | − | 0.815660i | 0.169816 | − | 0.985476i | \(-0.445683\pi\) |
−0.985476 | + | 0.169816i | \(0.945683\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 8.46637 | + | 8.46637i | 0.655147 | + | 0.655147i | 0.954228 | − | 0.299080i | \(-0.0966799\pi\) |
−0.299080 | + | 0.954228i | \(0.596680\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 4.42736i | − | 0.340566i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 9.58389i | 0.732899i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −8.19971 | + | 8.19971i | −0.623412 | + | 0.623412i | −0.946402 | − | 0.322990i | \(-0.895312\pi\) |
0.322990 | + | 0.946402i | \(0.395312\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.77545 | + | 3.77545i | −0.283780 | + | 0.283780i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 15.9103i | 1.18919i | 0.804025 | + | 0.594595i | \(0.202688\pi\) | ||||
−0.804025 | + | 0.594595i | \(0.797312\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 15.5721i | 1.15746i | 0.815518 | + | 0.578732i | \(0.196452\pi\) | ||||
−0.815518 | + | 0.578732i | \(0.803548\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.43955 | + | 1.43955i | 0.106415 | + | 0.106415i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 19.8648 | + | 19.8648i | 1.45266 | + | 1.45266i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.17850 | − | 7.60010i | 0.303941 | − | 0.552826i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.52605 | 0.472209 | 0.236104 | − | 0.971728i | \(-0.424129\pi\) | ||||
0.236104 | + | 0.971728i | \(0.424129\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.64028 | − | 4.64028i | −0.334014 | − | 0.334014i | 0.520094 | − | 0.854109i | \(-0.325897\pi\) |
−0.854109 | + | 0.520094i | \(0.825897\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 7.95497 | − | 7.95497i | 0.566768 | − | 0.566768i | −0.364453 | − | 0.931222i | \(-0.618744\pi\) |
0.931222 | + | 0.364453i | \(0.118744\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.84512 | −0.556126 | −0.278063 | − | 0.960563i | \(-0.589692\pi\) | ||||
−0.278063 | + | 0.960563i | \(0.589692\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.39750i | 0.0985720i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 13.5885 | − | 3.94736i | 0.953723 | − | 0.277050i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.126030 | − | 0.126030i | 0.00875969 | − | 0.00875969i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −12.7633 | −0.882859 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.9461 | −0.960091 | −0.480045 | − | 0.877244i | \(-0.659380\pi\) | ||||
−0.480045 | + | 0.877244i | \(0.659380\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3.49622 | − | 3.49622i | 0.239557 | − | 0.239557i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 26.4041 | − | 7.67022i | 1.79243 | − | 0.520689i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 1.99270i | − | 0.134654i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 33.0420 | 2.22265 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.17116 | + | 3.17116i | −0.212357 | + | 0.212357i | −0.805268 | − | 0.592911i | \(-0.797979\pi\) |
0.592911 | + | 0.805268i | \(0.297979\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.25072 | + | 2.25072i | 0.149386 | + | 0.149386i | 0.777844 | − | 0.628458i | \(-0.216314\pi\) |
−0.628458 | + | 0.777844i | \(0.716314\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −12.1177 | −0.800758 | −0.400379 | − | 0.916350i | \(-0.631122\pi\) | ||||
−0.400379 | + | 0.916350i | \(0.631122\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.76162 | + | 2.61791i | 0.313291 | + | 0.172246i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −4.60978 | − | 4.60978i | −0.301996 | − | 0.301996i | 0.539798 | − | 0.841795i | \(-0.318501\pi\) |
−0.841795 | + | 0.539798i | \(0.818501\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2.34331 | − | 2.34331i | −0.152215 | − | 0.152215i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0.804297i | 0.0520257i | 0.999662 | + | 0.0260128i | \(0.00828108\pi\) | ||||
−0.999662 | + | 0.0260128i | \(0.991719\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 17.1249i | − | 1.10311i | −0.834138 | − | 0.551555i | \(-0.814035\pi\) | ||
0.834138 | − | 0.551555i | \(-0.185965\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 9.44923 | − | 9.44923i | 0.606169 | − | 0.606169i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −10.6149 | + | 10.6149i | −0.675411 | + | 0.675411i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 1.67412i | − | 0.106093i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 12.6371i | 0.797645i | 0.917028 | + | 0.398822i | \(0.130581\pi\) | ||||
−0.917028 | + | 0.398822i | \(0.869419\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.167840 | + | 0.167840i | 0.0105520 | + | 0.0105520i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6.59946 | + | 6.59946i | 0.411663 | + | 0.411663i | 0.882318 | − | 0.470655i | \(-0.155982\pi\) |
−0.470655 | + | 0.882318i | \(0.655982\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −25.5767 | − | 14.0620i | −1.58926 | − | 0.873767i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 14.2541 | 0.882306 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 7.56907 | + | 7.56907i | 0.466729 | + | 0.466729i | 0.900853 | − | 0.434124i | \(-0.142942\pi\) |
−0.434124 | + | 0.900853i | \(0.642942\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.34955 | − | 3.34955i | 0.204989 | − | 0.204989i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 22.1148 | 1.34836 | 0.674181 | − | 0.738566i | \(-0.264497\pi\) | ||||
0.674181 | + | 0.738566i | \(0.264497\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 29.7020i | 1.80427i | 0.431456 | + | 0.902134i | \(0.358000\pi\) | ||||
−0.431456 | + | 0.902134i | \(0.642000\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 6.13735 | − | 1.78286i | 0.371450 | − | 0.107904i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.38005 | + | 3.38005i | −0.203087 | + | 0.203087i | −0.801321 | − | 0.598234i | \(-0.795869\pi\) |
0.598234 | + | 0.801321i | \(0.295869\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 27.6975 | 1.65821 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −26.0224 | −1.55237 | −0.776184 | − | 0.630507i | \(-0.782847\pi\) | ||||
−0.776184 | + | 0.630507i | \(0.782847\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −13.9610 | + | 13.9610i | −0.829895 | + | 0.829895i | −0.987502 | − | 0.157607i | \(-0.949622\pi\) |
0.157607 | + | 0.987502i | \(0.449622\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 14.3275 | − | 4.16203i | 0.845724 | − | 0.245677i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 45.6472i | 2.68513i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.09869 | 0.298891 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −6.51568 | + | 6.51568i | −0.380650 | + | 0.380650i | −0.871336 | − | 0.490686i | \(-0.836746\pi\) |
0.490686 | + | 0.871336i | \(0.336746\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 8.22726 | + | 8.22726i | 0.477394 | + | 0.477394i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.279177 | 0.0161452 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −12.5081 | + | 22.7505i | −0.720957 | + | 1.31132i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −5.64102 | − | 5.64102i | −0.324068 | − | 0.324068i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6.13557 | + | 6.13557i | 0.350176 | + | 0.350176i | 0.860175 | − | 0.509999i | \(-0.170354\pi\) |
−0.509999 | + | 0.860175i | \(0.670354\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 8.49022i | − | 0.482992i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 1.36872i | − | 0.0776131i | −0.999247 | − | 0.0388065i | \(-0.987644\pi\) | ||
0.999247 | − | 0.0388065i | \(-0.0123556\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 13.9335 | − | 13.9335i | 0.787565 | − | 0.787565i | −0.193529 | − | 0.981095i | \(-0.561993\pi\) |
0.981095 | + | 0.193529i | \(0.0619934\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −8.42849 | + | 8.42849i | −0.473391 | + | 0.473391i | −0.903010 | − | 0.429619i | \(-0.858648\pi\) |
0.429619 | + | 0.903010i | \(0.358648\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 18.9829i | 1.06284i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 3.72224i | − | 0.207755i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −20.1257 | − | 20.1257i | −1.11983 | − | 1.11983i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.54002 | − | 1.54002i | −0.0851635 | − | 0.0851635i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 6.20714 | − | 11.2899i | 0.342211 | − | 0.622433i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 25.5762 | 1.40580 | 0.702899 | − | 0.711290i | \(-0.251889\pi\) | ||||
0.702899 | + | 0.711290i | \(0.251889\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −20.7902 | − | 20.7902i | −1.13929 | − | 1.13929i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 19.0296 | − | 19.0296i | 1.03661 | − | 1.03661i | 0.0373062 | − | 0.999304i | \(-0.488122\pi\) |
0.999304 | − | 0.0373062i | \(-0.0118777\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.95254 | 0.214672 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 36.8862i | 1.99750i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −13.8911 | − | 12.2490i | −0.750049 | − | 0.661382i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 10.1175 | − | 10.1175i | 0.543135 | − | 0.543135i | −0.381311 | − | 0.924447i | \(-0.624527\pi\) |
0.924447 | + | 0.381311i | \(0.124527\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −17.7082 | −0.947898 | −0.473949 | − | 0.880552i | \(-0.657172\pi\) | ||||
−0.473949 | + | 0.880552i | \(0.657172\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 13.6848 | 0.730439 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 18.8566 | − | 18.8566i | 1.00363 | − | 1.00363i | 0.00364095 | − | 0.999993i | \(-0.498841\pi\) |
0.999993 | − | 0.00364095i | \(-0.00115895\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.38027 | + | 11.6363i | 0.178903 | + | 0.615860i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 15.0844i | 0.796123i | 0.917359 | + | 0.398061i | \(0.130317\pi\) | ||||
−0.917359 | + | 0.398061i | \(0.869683\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.06900 | −0.319421 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.653777 | + | 0.653777i | −0.0343144 | + | 0.0343144i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5.09830 | − | 5.09830i | −0.266129 | − | 0.266129i | 0.561409 | − | 0.827538i | \(-0.310259\pi\) |
−0.827538 | + | 0.561409i | \(0.810259\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 15.0293 | 0.782393 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.16601 | − | 2.12082i | 0.0605365 | − | 0.110107i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12.5295 | + | 12.5295i | 0.648754 | + | 0.648754i | 0.952692 | − | 0.303938i | \(-0.0983016\pi\) |
−0.303938 | + | 0.952692i | \(0.598302\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 15.7875 | + | 15.7875i | 0.813099 | + | 0.813099i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 28.0665i | − | 1.44168i | −0.693103 | − | 0.720838i | \(-0.743757\pi\) | ||
0.693103 | − | 0.720838i | \(-0.256243\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 8.07004i | 0.413441i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 19.4556 | − | 19.4556i | 0.994136 | − | 0.994136i | −0.00584671 | − | 0.999983i | \(-0.501861\pi\) |
0.999983 | + | 0.00584671i | \(0.00186108\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −18.4929 | + | 18.4929i | −0.940046 | + | 0.940046i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 35.4128i | − | 1.79550i | −0.440505 | − | 0.897750i | \(-0.645201\pi\) | ||
0.440505 | − | 0.897750i | \(-0.354799\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.529315i | 0.0267686i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.65685 | + | 5.65685i | 0.285351 | + | 0.285351i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 13.0002 | + | 13.0002i | 0.652460 | + | 0.652460i | 0.953585 | − | 0.301124i | \(-0.0973620\pi\) |
−0.301124 | + | 0.953585i | \(0.597362\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4.82416 | − | 2.65230i | −0.241510 | − | 0.132781i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 26.6516 | 1.33092 | 0.665460 | − | 0.746434i | \(-0.268236\pi\) | ||||
0.665460 | + | 0.746434i | \(0.268236\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 30.6772 | + | 30.6772i | 1.52814 | + | 1.52814i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 27.6873 | − | 27.6873i | 1.37241 | − | 1.37241i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −24.9874 | −1.23555 | −0.617775 | − | 0.786355i | \(-0.711966\pi\) | ||||
−0.617775 | + | 0.786355i | \(0.711966\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 10.8653i | − | 0.535946i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 6.81034 | + | 23.4441i | 0.335115 | + | 1.15361i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3.09261 | + | 3.09261i | −0.151446 | + | 0.151446i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −29.7544 | −1.45360 | −0.726799 | − | 0.686850i | \(-0.758993\pi\) | ||||
−0.726799 | + | 0.686850i | \(0.758993\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.60400 | 0.321859 | 0.160930 | − | 0.986966i | \(-0.448551\pi\) | ||||
0.160930 | + | 0.986966i | \(0.448551\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 9.17707 | − | 9.17707i | 0.446204 | − | 0.446204i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.93906 | − | 2.59674i | 0.432592 | − | 0.125665i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 8.57378i | 0.413946i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −18.0134 | −0.867677 | −0.433839 | − | 0.900991i | \(-0.642841\pi\) | ||||
−0.433839 | + | 0.900991i | \(0.642841\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.25124 | − | 3.25124i | 0.156244 | − | 0.156244i | −0.624656 | − | 0.780900i | \(-0.714761\pi\) |
0.780900 | + | 0.624656i | \(0.214761\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.170045 | − | 0.170045i | −0.00813436 | − | 0.00813436i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −11.5574 | −0.551607 | −0.275803 | − | 0.961214i | \(-0.588944\pi\) | ||||
−0.275803 | + | 0.961214i | \(0.588944\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −9.99553 | − | 15.7526i | −0.475978 | − | 0.750124i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −22.0498 | − | 22.0498i | −1.04762 | − | 1.04762i | −0.998808 | − | 0.0488073i | \(-0.984458\pi\) |
−0.0488073 | − | 0.998808i | \(-0.515542\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −7.03397 | − | 7.03397i | −0.332695 | − | 0.332695i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 22.8564i | − | 1.07866i | −0.842094 | − | 0.539330i | \(-0.818677\pi\) | ||
0.842094 | − | 0.539330i | \(-0.181323\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 20.0152i | 0.942480i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2.78735 | + | 2.78735i | −0.130961 | + | 0.130961i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.19406 | − | 6.19406i | 0.289746 | − | 0.289746i | −0.547234 | − | 0.836980i | \(-0.684319\pi\) |
0.836980 | + | 0.547234i | \(0.184319\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 25.9461i | 1.21106i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 9.63815i | − | 0.448893i | −0.974486 | − | 0.224447i | \(-0.927943\pi\) | ||
0.974486 | − | 0.224447i | \(-0.0720575\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 25.9680 | + | 25.9680i | 1.20684 | + | 1.20684i | 0.972046 | + | 0.234791i | \(0.0754404\pi\) |
0.234791 | + | 0.972046i | \(0.424560\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −20.6556 | − | 20.6556i | −0.955825 | − | 0.955825i | 0.0432393 | − | 0.999065i | \(-0.486232\pi\) |
−0.999065 | + | 0.0432393i | \(0.986232\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.59939 | + | 3.07852i | 0.258556 | + | 0.142153i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.941650 | 0.0433889 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −24.6279 | − | 24.6279i | −1.13239 | − | 1.13239i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.72392 | − | 1.72392i | 0.0789327 | − | 0.0789327i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −8.74688 | −0.399655 | −0.199828 | − | 0.979831i | \(-0.564038\pi\) | ||||
−0.199828 | + | 0.979831i | \(0.564038\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 46.0535i | − | 2.09986i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.0285604 | + | 0.0983170i | 0.00129954 | + | 0.00447358i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.18084 | − | 6.18084i | 0.280081 | − | 0.280081i | −0.553061 | − | 0.833141i | \(-0.686540\pi\) |
0.833141 | + | 0.553061i | \(0.186540\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 8.52170 | 0.385365 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −11.4596 | −0.517166 | −0.258583 | − | 0.965989i | \(-0.583256\pi\) | ||||
−0.258583 | + | 0.965989i | \(0.583256\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −29.9329 | + | 29.9329i | −1.34811 | + | 1.34811i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −6.30665 | − | 21.7101i | −0.282892 | − | 0.973833i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 37.1794i | 1.66438i | 0.554493 | + | 0.832189i | \(0.312912\pi\) | ||||
−0.554493 | + | 0.832189i | \(0.687088\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.92820 | −0.309529 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 6.72761 | − | 6.72761i | 0.299969 | − | 0.299969i | −0.541032 | − | 0.841002i | \(-0.681966\pi\) |
0.841002 | + | 0.541032i | \(0.181966\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.81150 | + | 1.81150i | 0.0804516 | + | 0.0804516i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 42.5874 | 1.88765 | 0.943826 | − | 0.330442i | \(-0.107198\pi\) | ||||
0.943826 | + | 0.330442i | \(0.107198\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.98421 | − | 4.38968i | −0.353201 | − | 0.194188i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −8.33533 | − | 8.33533i | −0.368014 | − | 0.368014i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 12.2216 | + | 12.2216i | 0.537503 | + | 0.537503i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 6.70999i | − | 0.294536i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 18.0438i | 0.790512i | 0.918571 | + | 0.395256i | \(0.129344\pi\) | ||||
−0.918571 | + | 0.395256i | \(0.870656\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −19.0355 | + | 19.0355i | −0.832363 | + | 0.832363i | −0.987840 | − | 0.155477i | \(-0.950309\pi\) |
0.155477 | + | 0.987840i | \(0.450309\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −58.1635 | + | 58.1635i | −2.53364 | + | 2.53364i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 22.9955i | − | 0.999806i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 24.5924i | 1.06722i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 16.6461 | + | 16.6461i | 0.721024 | + | 0.721024i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −6.50985 | − | 6.50985i | −0.280921 | − | 0.280921i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 20.9785 | − | 13.3115i | 0.903608 | − | 0.573368i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.51876 | −0.151283 | −0.0756416 | − | 0.997135i | \(-0.524100\pi\) | ||||
−0.0756416 | + | 0.997135i | \(0.524100\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −6.37147 | − | 6.37147i | −0.273426 | − | 0.273426i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −10.4209 | + | 10.4209i | −0.445564 | + | 0.445564i | −0.893877 | − | 0.448313i | \(-0.852025\pi\) |
0.448313 | + | 0.893877i | \(0.352025\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 9.37693 | 0.400198 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 19.2322i | − | 0.819320i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −14.5510 | + | 4.22698i | −0.618773 | + | 0.179749i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.59156 | − | 1.59156i | 0.0674367 | − | 0.0674367i | −0.672584 | − | 0.740021i | \(-0.734816\pi\) |
0.740021 | + | 0.672584i | \(0.234816\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −40.9647 | −1.73262 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −16.2558 | −0.686319 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 12.0816 | − | 12.0816i | 0.509178 | − | 0.509178i | −0.405096 | − | 0.914274i | \(-0.632762\pi\) |
0.914274 | + | 0.405096i | \(0.132762\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −4.50121 | − | 15.4951i | −0.189033 | − | 0.650732i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 29.0881i | 1.21944i | 0.792619 | + | 0.609718i | \(0.208717\pi\) | ||||
−0.792619 | + | 0.609718i | \(0.791283\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.95879 | 0.249368 | 0.124684 | − | 0.992197i | \(-0.460208\pi\) | ||||
0.124684 | + | 0.992197i | \(0.460208\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −2.67020 | + | 2.67020i | −0.111549 | + | 0.111549i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 14.6203 | + | 14.6203i | 0.608650 | + | 0.608650i | 0.942593 | − | 0.333943i | \(-0.108379\pi\) |
−0.333943 | + | 0.942593i | \(0.608379\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3.79723 | 0.157808 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.70774 | − | 3.68788i | −0.278284 | − | 0.152999i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.29582 | + | 2.29582i | 0.0950833 | + | 0.0950833i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −23.5748 | − | 23.5748i | −0.973035 | − | 0.973035i | 0.0266107 | − | 0.999646i | \(-0.491529\pi\) |
−0.999646 | + | 0.0266107i | \(0.991529\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 37.3707i | − | 1.53983i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6.50972i | 0.267774i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −6.48482 | + | 6.48482i | −0.266300 | + | 0.266300i | −0.827607 | − | 0.561308i | \(-0.810299\pi\) |
0.561308 | + | 0.827607i | \(0.310299\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3.20991 | − | 3.20991i | 0.131373 | − | 0.131373i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 26.8124i | 1.09552i | 0.836634 | + | 0.547762i | \(0.184520\pi\) | ||||
−0.836634 | + | 0.547762i | \(0.815480\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 42.1513i | − | 1.71939i | −0.510811 | − | 0.859693i | \(-0.670655\pi\) | ||
0.510811 | − | 0.859693i | \(-0.329345\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.55150 | + | 4.55150i | 0.185351 | + | 0.185351i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −21.1320 | − | 21.1320i | −0.857720 | − | 0.857720i | 0.133349 | − | 0.991069i | \(-0.457427\pi\) |
−0.991069 | + | 0.133349i | \(0.957427\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.94476 | + | 7.17496i | −0.159850 | + | 0.290744i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 20.3287 | 0.822410 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.374096 | + | 0.374096i | 0.0151096 | + | 0.0151096i | 0.714621 | − | 0.699512i | \(-0.246599\pi\) |
−0.699512 | + | 0.714621i | \(0.746599\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −10.3289 | + | 10.3289i | −0.415826 | + | 0.415826i | −0.883762 | − | 0.467936i | \(-0.844998\pi\) |
0.467936 | + | 0.883762i | \(0.344998\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9.30472 | −0.373988 | −0.186994 | − | 0.982361i | \(-0.559875\pi\) | ||||
−0.186994 | + | 0.982361i | \(0.559875\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.219222i | 0.00879709i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6.04206 | − | 20.7993i | −0.242070 | − | 0.833308i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 5.22225 | − | 5.22225i | 0.208557 | − | 0.208557i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 87.3168 | 3.48155 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.74964 | 0.268699 | 0.134349 | − | 0.990934i | \(-0.457106\pi\) | ||||
0.134349 | + | 0.990934i | \(0.457106\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 5.70620 | − | 5.70620i | 0.226801 | − | 0.226801i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.37642 | − | 28.5181i | 0.252643 | − | 1.12993i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 22.7736i | − | 0.900909i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −12.2287 | −0.483006 | −0.241503 | − | 0.970400i | \(-0.577640\pi\) | ||||
−0.241503 | + | 0.970400i | \(0.577640\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5.61879 | + | 5.61879i | −0.221584 | + | 0.221584i | −0.809165 | − | 0.587581i | \(-0.800080\pi\) |
0.587581 | + | 0.809165i | \(0.300080\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 5.37047 | + | 5.37047i | 0.211135 | + | 0.211135i | 0.804749 | − | 0.593615i | \(-0.202300\pi\) |
−0.593615 | + | 0.804749i | \(0.702300\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −32.7510 | −1.28559 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −7.66518 | + | 13.9419i | −0.300422 | + | 0.546425i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 20.1562 | + | 20.1562i | 0.788774 | + | 0.788774i | 0.981293 | − | 0.192519i | \(-0.0616657\pi\) |
−0.192519 | + | 0.981293i | \(0.561666\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −6.49001 | − | 6.49001i | −0.253199 | − | 0.253199i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 0.712783i | − | 0.0277661i | −0.999904 | − | 0.0138830i | \(-0.995581\pi\) | ||
0.999904 | − | 0.0138830i | \(-0.00441925\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 28.3507i | − | 1.10271i | −0.834269 | − | 0.551357i | \(-0.814110\pi\) | ||
0.834269 | − | 0.551357i | \(-0.185890\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −13.5195 | + | 13.5195i | −0.525053 | + | 0.525053i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.252907 | + | 0.252907i | −0.00979261 | + | 0.00979261i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 2.59503i | − | 0.100330i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 12.4877i | 0.482083i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5.58066 | − | 5.58066i | −0.215119 | − | 0.215119i | 0.591319 | − | 0.806438i | \(-0.298607\pi\) |
−0.806438 | + | 0.591319i | \(0.798607\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −8.82232 | − | 8.82232i | −0.339069 | − | 0.339069i | 0.516948 | − | 0.856017i | \(-0.327068\pi\) |
−0.856017 | + | 0.516948i | \(0.827068\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 11.2318 | − | 20.4290i | 0.431037 | − | 0.783995i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.84181 | −0.0705784 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 6.51153 | + | 6.51153i | 0.249157 | + | 0.249157i | 0.820625 | − | 0.571468i | \(-0.193626\pi\) |
−0.571468 | + | 0.820625i | \(0.693626\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.95807 | − | 4.95807i | 0.189162 | − | 0.189162i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.81875 | 0.145483 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 26.2458i | 0.998436i | 0.866476 | + | 0.499218i | \(0.166379\pi\) | ||||
−0.866476 | + | 0.499218i | \(0.833621\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 24.0343 | − | 6.98179i | 0.912987 | − | 0.265216i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −31.5608 | + | 31.5608i | −1.19545 | + | 1.19545i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 3.77227 | 0.142680 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −12.5261 | −0.473103 | −0.236551 | − | 0.971619i | \(-0.576017\pi\) | ||||
−0.236551 | + | 0.971619i | \(0.576017\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −28.0510 | + | 28.0510i | −1.05796 | + | 1.05796i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −35.0285 | + | 10.1755i | −1.31738 | + | 0.382690i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 32.8204i | 1.23260i | 0.787512 | + | 0.616299i | \(0.211369\pi\) | ||||
−0.787512 | + | 0.616299i | \(0.788631\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −15.2638 | −0.572437 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −0.491432 | + | 0.491432i | −0.0184043 | + | 0.0184043i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −0.329086 | − | 0.329086i | −0.0122900 | − | 0.0122900i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −19.4184 | −0.724186 | −0.362093 | − | 0.932142i | \(-0.617938\pi\) | ||||
−0.362093 | + | 0.932142i | \(0.617938\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −34.0179 | − | 18.7029i | −1.26689 | − | 0.696533i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 7.00682 | + | 7.00682i | 0.260586 | + | 0.260586i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −5.73374 | − | 5.73374i | −0.212653 | − | 0.212653i | 0.592741 | − | 0.805393i | \(-0.298046\pi\) |
−0.805393 | + | 0.592741i | \(0.798046\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 10.5636i | − | 0.391243i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 77.6685i | − | 2.87267i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −8.52329 | + | 8.52329i | −0.314815 | + | 0.314815i | −0.846772 | − | 0.531957i | \(-0.821457\pi\) |
0.531957 | + | 0.846772i | \(0.321457\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −6.06145 | + | 6.06145i | −0.223276 | + | 0.223276i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 42.1938i | 1.55212i | 0.630656 | + | 0.776062i | \(0.282786\pi\) | ||||
−0.630656 | + | 0.776062i | \(0.717214\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 8.68641i | − | 0.319103i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −4.65010 | − | 4.65010i | −0.170596 | − | 0.170596i | 0.616645 | − | 0.787241i | \(-0.288491\pi\) |
−0.787241 | + | 0.616645i | \(0.788491\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −5.45242 | − | 5.45242i | −0.199494 | − | 0.199494i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −14.9140 | − | 8.19963i | −0.544945 | − | 0.299608i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12.7801 | −0.466353 | −0.233176 | − | 0.972434i | \(-0.574912\pi\) | ||||
−0.233176 | + | 0.972434i | \(0.574912\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −5.17059 | − | 5.17059i | −0.188427 | − | 0.188427i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 10.6724 | − | 10.6724i | 0.387893 | − | 0.387893i | −0.486042 | − | 0.873935i | \(-0.661560\pi\) |
0.873935 | + | 0.486042i | \(0.161560\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.137347 | −0.00498539 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 28.1860i | − | 1.02174i | −0.859657 | − | 0.510871i | \(-0.829323\pi\) | ||
0.859657 | − | 0.510871i | \(-0.170677\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −9.56294 | + | 2.77797i | −0.346201 | + | 0.100569i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −27.2381 | + | 27.2381i | −0.983510 | + | 0.983510i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −14.1998 | −0.512058 | −0.256029 | − | 0.966669i | \(-0.582414\pi\) | ||||
−0.256029 | + | 0.966669i | \(0.582414\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5.40047 | −0.194493 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −34.8461 | + | 34.8461i | −1.25333 | + | 1.25333i | −0.299110 | + | 0.954219i | \(0.596690\pi\) |
−0.954219 | + | 0.299110i | \(0.903310\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 16.2186 | − | 4.71138i | 0.581838 | − | 0.169020i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 20.2782i | − | 0.726540i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 30.3287 | 1.08525 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −12.3971 | + | 12.3971i | −0.443036 | + | 0.443036i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −19.6599 | − | 19.6599i | −0.700799 | − | 0.700799i | 0.263783 | − | 0.964582i | \(-0.415030\pi\) |
−0.964582 | + | 0.263783i | \(0.915030\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −6.19393 | −0.220510 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 8.70696 | − | 15.8367i | 0.309584 | − | 0.563089i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 10.3857 | + | 10.3857i | 0.368807 | + | 0.368807i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −15.8992 | − | 15.8992i | −0.563178 | − | 0.563178i | 0.367031 | − | 0.930209i | \(-0.380374\pi\) |
−0.930209 | + | 0.367031i | \(0.880374\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 38.5429i | 1.36355i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 21.8182i | − | 0.770907i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 8.64306 | − | 8.64306i | 0.305007 | − | 0.305007i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −9.04849 | + | 9.04849i | −0.318522 | + | 0.318522i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 3.53959i | − | 0.124445i | −0.998062 | − | 0.0622227i | \(-0.980181\pi\) | ||
0.998062 | − | 0.0622227i | \(-0.0198189\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 48.2187i | − | 1.69319i | −0.532240 | − | 0.846593i | \(-0.678650\pi\) | ||
0.532240 | − | 0.846593i | \(-0.321350\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −12.1529 | − | 12.1529i | −0.426220 | − | 0.426220i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 24.9514 | + | 24.9514i | 0.872939 | + | 0.872939i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 14.1821 | − | 25.7952i | 0.495562 | − | 0.901358i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 19.7728 | 0.690077 | 0.345038 | − | 0.938589i | \(-0.387866\pi\) | ||||
0.345038 | + | 0.938589i | \(0.387866\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 29.9476 | + | 29.9476i | 1.04391 | + | 1.04391i | 0.998991 | + | 0.0449175i | \(0.0143025\pi\) |
0.0449175 | + | 0.998991i | \(0.485697\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 3.77895 | − | 3.77895i | 0.131407 | − | 0.131407i | −0.638344 | − | 0.769751i | \(-0.720380\pi\) |
0.769751 | + | 0.638344i | \(0.220380\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 17.2917 | 0.600564 | 0.300282 | − | 0.953850i | \(-0.402919\pi\) | ||||
0.300282 | + | 0.953850i | \(0.402919\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 2.76596i | − | 0.0959501i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 54.0699 | + | 12.0896i | 1.87341 | + | 0.418879i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −24.0892 | + | 24.0892i | −0.832644 | + | 0.832644i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 13.5329 | 0.467207 | 0.233603 | − | 0.972332i | \(-0.424948\pi\) | ||||
0.233603 | + | 0.972332i | \(0.424948\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.395998 | 0.0136551 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 10.6473 | − | 10.6473i | 0.366714 | − | 0.366714i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.17931 | + | 4.05970i | 0.0405217 | + | 0.139493i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 11.4246i | − | 0.392090i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.737751 | 0.0252898 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −25.8248 | + | 25.8248i | −0.884225 | + | 0.884225i | −0.993961 | − | 0.109736i | \(-0.964999\pi\) |
0.109736 | + | 0.993961i | \(0.464999\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −36.0854 | − | 36.0854i | −1.23265 | − | 1.23265i | −0.962941 | − | 0.269711i | \(-0.913072\pi\) |
−0.269711 | − | 0.962941i | \(-0.586928\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.18630 | 0.245193 | 0.122597 | − | 0.992457i | \(-0.460878\pi\) | ||||
0.122597 | + | 0.992457i | \(0.460878\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.15929 | + | 7.56517i | −0.141748 | + | 0.257820i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −20.2042 | − | 20.2042i | −0.687758 | − | 0.687758i | 0.273978 | − | 0.961736i | \(-0.411660\pi\) |
−0.961736 | + | 0.273978i | \(0.911660\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −18.6770 | − | 18.6770i | −0.634304 | − | 0.634304i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 20.3276i | − | 0.689565i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 10.0823i | 0.341625i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 16.6059 | − | 16.6059i | 0.562023 | − | 0.562023i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −15.5068 | + | 15.5068i | −0.523626 | + | 0.523626i | −0.918665 | − | 0.395038i | \(-0.870731\pi\) |
0.395038 | + | 0.918665i | \(0.370731\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 5.33191i | − | 0.179841i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 35.4110i | 1.19303i | 0.802603 | + | 0.596513i | \(0.203448\pi\) | ||||
−0.802603 | + | 0.596513i | \(0.796552\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 29.1344 | + | 29.1344i | 0.980449 | + | 0.980449i | 0.999813 | − | 0.0193631i | \(-0.00616386\pi\) |
−0.0193631 | + | 0.999813i | \(0.506164\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 27.6553 | + | 27.6553i | 0.928575 | + | 0.928575i | 0.997614 | − | 0.0690386i | \(-0.0219932\pi\) |
−0.0690386 | + | 0.997614i | \(0.521993\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 32.3344 | + | 17.7773i | 1.08446 | + | 0.596232i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 21.6464 | 0.725180 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −12.3821 | − | 12.3821i | −0.414351 | − | 0.414351i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.114228 | + | 0.114228i | −0.00381396 | + | 0.00381396i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −55.5813 | −1.85374 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7.24029i | 0.241209i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −4.19078 | − | 14.4264i | −0.139461 | − | 0.480082i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 12.7400 | − | 12.7400i | 0.423024 | − | 0.423024i | −0.463220 | − | 0.886244i | \(-0.653306\pi\) |
0.886244 | + | 0.463220i | \(0.153306\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −36.7443 | −1.21873 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −16.1219 | −0.534142 | −0.267071 | − | 0.963677i | \(-0.586056\pi\) | ||||
−0.267071 | + | 0.963677i | \(0.586056\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7.26125 | − | 7.26125i | 0.240312 | − | 0.240312i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 35.1268 | − | 10.2041i | 1.15999 | − | 0.336969i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 10.2370i | − | 0.337689i | −0.985643 | − | 0.168844i | \(-0.945997\pi\) | ||
0.985643 | − | 0.168844i | \(-0.0540035\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −5.02086 | −0.165443 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 25.2236 | − | 25.2236i | 0.830244 | − | 0.830244i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −27.6517 | − | 27.6517i | −0.908200 | − | 0.908200i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 41.9048 | 1.37485 | 0.687427 | − | 0.726254i | \(-0.258740\pi\) | ||||
0.687427 | + | 0.726254i | \(0.258740\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −21.2541 | + | 13.4864i | −0.696574 | + | 0.441999i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0.560026 | + | 0.560026i | 0.0183344 | + | 0.0183344i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 13.6396 | + | 13.6396i | 0.445587 | + | 0.445587i | 0.893884 | − | 0.448298i | \(-0.147970\pi\) |
−0.448298 | + | 0.893884i | \(0.647970\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 11.4020i | 0.372091i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 12.4316i | 0.405258i | 0.979256 | + | 0.202629i | \(0.0649486\pi\) | ||||
−0.979256 | + | 0.202629i | \(0.935051\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.266662 | + | 0.266662i | −0.00868370 | + | 0.00868370i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 32.8423 | − | 32.8423i | 1.06723 | − | 1.06723i | 0.0696622 | − | 0.997571i | \(-0.477808\pi\) |
0.997571 | − | 0.0696622i | \(-0.0221922\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 14.3764i | − | 0.466678i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 6.89720i | − | 0.223657i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −19.7497 | − | 19.7497i | −0.639756 | − | 0.639756i | 0.310739 | − | 0.950495i | \(-0.399424\pi\) |
−0.950495 | + | 0.310739i | \(0.899424\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −7.76703 | − | 7.76703i | −0.251072 | − | 0.251072i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −43.5343 | − | 23.9349i | −1.40579 | − | 0.772899i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −77.0016 | −2.48392 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −12.1229 | − | 12.1229i | −0.390655 | − | 0.390655i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0.760423 | − | 0.760423i | 0.0244535 | − | 0.0244535i | −0.694774 | − | 0.719228i | \(-0.744496\pi\) |
0.719228 | + | 0.694774i | \(0.244496\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 16.4693 | 0.529070 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 35.7520i | 1.14733i | 0.819088 | + | 0.573667i | \(0.194480\pi\) | ||||
−0.819088 | + | 0.573667i | \(0.805520\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.57859 | + | 19.2039i | 0.178841 | + | 0.615647i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 22.3370 | − | 22.3370i | 0.714625 | − | 0.714625i | −0.252874 | − | 0.967499i | \(-0.581376\pi\) |
0.967499 | + | 0.252874i | \(0.0813757\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 29.0563 | 0.928644 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −10.0314 | −0.320277 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −21.6708 | + | 21.6708i | −0.691191 | + | 0.691191i | −0.962494 | − | 0.271303i | \(-0.912545\pi\) |
0.271303 | + | 0.962494i | \(0.412545\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.07967 | + | 7.15910i | 0.0661966 | + | 0.227877i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 0.656231i | − | 0.0208669i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 45.0277 | 1.43035 | 0.715176 | − | 0.698944i | \(-0.246347\pi\) | ||||
0.715176 | + | 0.698944i | \(0.246347\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −10.4648 | + | 10.4648i | −0.332090 | + | 0.332090i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 11.7911 | + | 11.7911i | 0.373427 | + | 0.373427i | 0.868724 | − | 0.495297i | \(-0.164941\pi\) |
−0.495297 | + | 0.868724i | \(0.664941\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 36.1634 | 1.14416 |
(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 | 1400.2.x.c.993.7 | yes | 32 | |
5.2 | odd | 4 | inner | 1400.2.x.c.657.9 | yes | 32 | |
5.3 | odd | 4 | inner | 1400.2.x.c.657.8 | yes | 32 | |
5.4 | even | 2 | inner | 1400.2.x.c.993.10 | yes | 32 | |
7.6 | odd | 2 | inner | 1400.2.x.c.993.9 | yes | 32 | |
35.13 | even | 4 | inner | 1400.2.x.c.657.10 | yes | 32 | |
35.27 | even | 4 | inner | 1400.2.x.c.657.7 | ✓ | 32 | |
35.34 | odd | 2 | inner | 1400.2.x.c.993.8 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1400.2.x.c.657.7 | ✓ | 32 | 35.27 | even | 4 | inner | |
1400.2.x.c.657.8 | yes | 32 | 5.3 | odd | 4 | inner | |
1400.2.x.c.657.9 | yes | 32 | 5.2 | odd | 4 | inner | |
1400.2.x.c.657.10 | yes | 32 | 35.13 | even | 4 | inner | |
1400.2.x.c.993.7 | yes | 32 | 1.1 | even | 1 | trivial | |
1400.2.x.c.993.8 | yes | 32 | 35.34 | odd | 2 | inner | |
1400.2.x.c.993.9 | yes | 32 | 7.6 | odd | 2 | inner | |
1400.2.x.c.993.10 | yes | 32 | 5.4 | even | 2 | inner |