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 | 993.8 | ||
Character | \(\chi\) | \(=\) | 1400.993 |
Dual form | 1400.2.x.c.657.8 |
$q$-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 | ||||||||
\(7\) | 2.54072 | + | 0.738062i | 0.960302 | + | 0.278961i | ||||
\(8\) | 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 | \(-0.635339\pi\) | ||||
−0.412486 | + | 0.910964i | \(0.635339\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.34155 | + | 0.737576i | −0.292750 | + | 0.160952i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.0472877 | + | 0.0472877i | 0.00986016 | + | 0.00986016i | 0.712020 | − | 0.702160i | \(-0.247781\pi\) |
−0.702160 | + | 0.712020i | \(0.747781\pi\) | |||||||
\(24\) | 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 | \(0.383052\pi\) | ||||
−0.359192 | + | 0.933264i | \(0.616948\pi\) | |||||||
\(32\) | 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 | \(-0.388510\pi\) |
0.939285 | − | 0.343137i | \(-0.111490\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 2.41560i | − | 0.386805i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.63913i | 0.880685i | 0.897830 | + | 0.440342i | \(0.145143\pi\) | ||||
−0.897830 | + | 0.440342i | \(0.854857\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.93871 | − | 6.93871i | −1.05814 | − | 1.05814i | −0.998202 | − | 0.0599420i | \(-0.980908\pi\) |
−0.0599420 | − | 0.998202i | \(-0.519092\pi\) | |||||||
\(44\) | 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 | 0.750134 | − | 0.661285i | \(-0.229989\pi\) |
−0.661285 | + | 0.750134i | \(0.729989\pi\) | |||||||
\(54\) | 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 | \(-0.705090\pi\) | ||||
−0.600648 | + | 0.799514i | \(0.705090\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.51832i | 0.450474i | 0.974304 | + | 0.225237i | \(0.0723157\pi\) | ||||
−0.974304 | + | 0.225237i | \(0.927684\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.96707 | + | 6.77147i | −0.247827 | + | 0.853125i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.70777 | + | 1.70777i | −0.208637 | + | 0.208637i | −0.803688 | − | 0.595051i | \(-0.797132\pi\) |
0.595051 | + | 0.803688i | \(0.297132\pi\) | |||||||
\(68\) | 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 | ||||||||
\(77\) | −9.01790 | − | 2.61964i | −1.02768 | − | 0.298535i | ||||
\(78\) | 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 | \(-0.357145\pi\) | ||||
0.433878 | + | 0.900972i | \(0.357145\pi\) | |||||||
\(90\) | 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 | \(-0.759400\pi\) | ||
0.727677 | − | 0.685920i | \(-0.240600\pi\) | |||||||
\(102\) | 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 | −0.452189 | − | 0.891922i | \(-0.649357\pi\) |
0.891922 | + | 0.452189i | \(0.149357\pi\) | |||||||
\(108\) | 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 | 0.896803 | − | 0.442429i | \(-0.145883\pi\) |
−0.442429 | + | 0.896803i | \(0.645883\pi\) | |||||||
\(114\) | 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 | −0.993021 | − | 0.117936i | \(-0.962372\pi\) |
0.117936 | + | 0.993021i | \(0.462372\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5.67809 | 0.499928 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 13.8255i | 1.20794i | 0.797006 | + | 0.603971i | \(0.206416\pi\) | ||||
−0.797006 | + | 0.603971i | \(0.793584\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −9.13636 | − | 2.65405i | −0.792223 | − | 0.230135i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 13.2776 | − | 13.2776i | 1.13438 | − | 1.13438i | 0.144938 | − | 0.989441i | \(-0.453702\pi\) |
0.989441 | − | 0.144938i | \(-0.0462984\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.55843 | −0.641097 | −0.320549 | − | 0.947232i | \(-0.603867\pi\) | ||||
−0.320549 | + | 0.947232i | \(0.603867\pi\) | |||||||
\(140\) | 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 | ||||||||
\(147\) | −3.95288 | + | 0.883831i | −0.326028 | + | 0.0728971i | ||||
\(148\) | 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 | 0.985476 | − | 0.169816i | \(-0.0543172\pi\) |
−0.169816 | + | 0.985476i | \(0.554317\pi\) | |||||||
\(164\) | 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 | \(-0.803548\pi\) | ||
0.815518 | − | 0.578732i | \(-0.196452\pi\) | |||||||
\(182\) | 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 | 0.854109 | − | 0.520094i | \(-0.174103\pi\) |
−0.520094 | + | 0.854109i | \(0.674103\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −7.95497 | + | 7.95497i | −0.566768 | + | 0.566768i | −0.931222 | − | 0.364453i | \(-0.881256\pi\) |
0.364453 | + | 0.931222i | \(0.381256\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.84512 | 0.556126 | 0.278063 | − | 0.960563i | \(-0.410308\pi\) | ||||
0.278063 | + | 0.960563i | \(0.410308\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 1.39750i | − | 0.0985720i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.94736 | − | 13.5885i | 0.277050 | − | 0.953723i | ||||
\(204\) | 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 | ||||||||
\(217\) | −7.67022 | + | 26.4041i | −0.520689 | + | 1.79243i | ||||
\(218\) | 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 | \(-0.368878\pi\) | ||||
0.400379 | + | 0.916350i | \(0.368878\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.76162 | − | 2.61791i | 0.313291 | − | 0.172246i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4.60978 | + | 4.60978i | 0.301996 | + | 0.301996i | 0.841795 | − | 0.539798i | \(-0.181499\pi\) |
−0.539798 | + | 0.841795i | \(0.681499\pi\) | |||||||
\(234\) | 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 | \(0.185965\pi\) | ||||
−0.834138 | + | 0.551555i | \(0.814035\pi\) | |||||||
\(242\) | 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 | \(-0.869419\pi\) | ||
0.917028 | − | 0.398822i | \(-0.130581\pi\) | |||||||
\(252\) | 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 | 0.434124 | − | 0.900853i | \(-0.357058\pi\) |
−0.900853 | + | 0.434124i | \(0.857058\pi\) | |||||||
\(264\) | 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 | \(-0.735503\pi\) | ||||
−0.674181 | + | 0.738566i | \(0.735503\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 29.7020i | − | 1.80427i | −0.431456 | − | 0.902134i | \(-0.642000\pi\) | ||
0.431456 | − | 0.902134i | \(-0.358000\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.78286 | − | 6.13735i | 0.107904 | − | 0.371450i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.38005 | − | 3.38005i | 0.203087 | − | 0.203087i | −0.598234 | − | 0.801321i | \(-0.704131\pi\) |
0.801321 | + | 0.598234i | \(0.204131\pi\) | |||||||
\(278\) | 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 | ||||||||
\(287\) | −4.16203 | + | 14.3275i | −0.245677 | + | 0.845724i | ||||
\(288\) | 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 | \(0.0123556\pi\) | ||||
−0.999247 | + | 0.0388065i | \(0.987644\pi\) | |||||||
\(312\) | 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 | −0.429619 | − | 0.903010i | \(-0.641352\pi\) |
0.903010 | + | 0.429619i | \(0.141352\pi\) | |||||||
\(318\) | 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 | \(0.511878\pi\) |
−0.999304 | + | 0.0373062i | \(0.988122\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3.95254 | −0.214672 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 36.8862i | − | 1.99750i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 12.2490 | + | 13.8911i | 0.661382 | + | 0.750049i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −10.1175 | + | 10.1175i | −0.543135 | + | 0.543135i | −0.924447 | − | 0.381311i | \(-0.875473\pi\) |
0.381311 | + | 0.924447i | \(0.375473\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 17.7082 | 0.947898 | 0.473949 | − | 0.880552i | \(-0.342828\pi\) | ||||
0.473949 | + | 0.880552i | \(0.342828\pi\) | |||||||
\(350\) | 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 | ||||||||
\(357\) | 11.6363 | + | 3.38027i | 0.615860 | + | 0.178903i | ||||
\(358\) | 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 | 0.303938 | − | 0.952692i | \(-0.401698\pi\) |
−0.952692 | + | 0.303938i | \(0.901698\pi\) | |||||||
\(374\) | 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 | \(-0.288034\pi\) | ||||
0.617775 | + | 0.786355i | \(0.288034\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 10.8653i | 0.535946i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −23.4441 | − | 6.81034i | −1.15361 | − | 0.335115i | ||||
\(414\) | 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 | \(-0.241007\pi\) | ||||
0.726799 | + | 0.686850i | \(0.241007\pi\) | |||||||
\(420\) | 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 | ||||||||
\(427\) | −2.59674 | + | 8.93906i | −0.125665 | + | 0.432592i | ||||
\(428\) | 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 | \(-0.411056\pi\) | ||||
0.275803 | + | 0.961214i | \(0.411056\pi\) | |||||||
\(440\) | 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 | \(0.0155420\pi\) |
0.0488073 | + | 0.998808i | \(0.484458\pi\) | |||||||
\(444\) | 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 | −0.836980 | − | 0.547234i | \(-0.815681\pi\) |
0.547234 | + | 0.836980i | \(0.315681\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 25.9461i | 1.21106i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9.63815i | 0.448893i | 0.974486 | + | 0.224447i | \(0.0720575\pi\) | ||||
−0.974486 | + | 0.224447i | \(0.927943\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −25.9680 | − | 25.9680i | −1.20684 | − | 1.20684i | −0.972046 | − | 0.234791i | \(-0.924560\pi\) |
−0.234791 | − | 0.972046i | \(-0.575440\pi\) | |||||||
\(464\) | 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 | \(-0.435962\pi\) | ||||
0.199828 | + | 0.979831i | \(0.435962\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 46.0535i | 2.09986i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.0983170 | − | 0.0285604i | −0.00447358 | − | 0.00129954i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6.18084 | + | 6.18084i | −0.280081 | + | 0.280081i | −0.833141 | − | 0.553061i | \(-0.813460\pi\) |
0.553061 | + | 0.833141i | \(0.313460\pi\) | |||||||
\(488\) | 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 | ||||||||
\(497\) | −21.7101 | − | 6.30665i | −0.973833 | − | 0.282892i | ||||
\(498\) | 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 | \(-0.892802\pi\) | ||||
−0.943826 | + | 0.330442i | \(0.892802\pi\) | |||||||
\(510\) | 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 | \(-0.870656\pi\) | ||
0.918571 | − | 0.395256i | \(-0.129344\pi\) | |||||||
\(522\) | 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 | −0.448313 | − | 0.893877i | \(-0.647975\pi\) |
0.893877 | + | 0.448313i | \(0.147975\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −9.37693 | −0.400198 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 19.2322i | 0.819320i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.22698 | + | 14.5510i | −0.179749 | + | 0.618773i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.59156 | + | 1.59156i | −0.0674367 | + | 0.0674367i | −0.740021 | − | 0.672584i | \(-0.765184\pi\) |
0.672584 | + | 0.740021i | \(0.265184\pi\) | |||||||
\(558\) | 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 | ||||||||
\(567\) | −15.4951 | − | 4.50121i | −0.650732 | − | 0.189033i | ||||
\(568\) | 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 | \(0.329345\pi\) | ||||
−0.510811 | + | 0.859693i | \(0.670655\pi\) | |||||||
\(602\) | 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 | 0.699512 | − | 0.714621i | \(-0.253401\pi\) |
−0.714621 | + | 0.699512i | \(0.753401\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 10.3289 | − | 10.3289i | 0.415826 | − | 0.415826i | −0.467936 | − | 0.883762i | \(-0.655002\pi\) |
0.883762 | + | 0.467936i | \(0.155002\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9.30472 | 0.373988 | 0.186994 | − | 0.982361i | \(-0.440125\pi\) | ||||
0.186994 | + | 0.982361i | \(0.440125\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 0.219222i | − | 0.00879709i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 20.7993 | + | 6.04206i | 0.833308 | + | 0.242070i | ||||
\(624\) | 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 | ||||||||
\(637\) | −28.5181 | + | 6.37642i | −1.12993 | + | 0.252643i | ||||
\(638\) | 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 | 0.192519 | − | 0.981293i | \(-0.438334\pi\) |
−0.981293 | + | 0.192519i | \(0.938334\pi\) | |||||||
\(654\) | 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 | \(0.185890\pi\) | ||||
−0.834269 | + | 0.551357i | \(0.814110\pi\) | |||||||
\(662\) | 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 | 0.806438 | − | 0.591319i | \(-0.201393\pi\) |
−0.591319 | + | 0.806438i | \(0.701393\pi\) | |||||||
\(674\) | 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 | 0.571468 | − | 0.820625i | \(-0.306374\pi\) |
−0.820625 | + | 0.571468i | \(0.806374\pi\) | |||||||
\(684\) | 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 | \(-0.833621\pi\) | ||
0.866476 | − | 0.499218i | \(-0.166379\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 6.98179 | − | 24.0343i | 0.265216 | − | 0.912987i | ||||
\(694\) | 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 | ||||||||
\(707\) | 10.1755 | − | 35.0285i | 0.382690 | − | 1.31738i | ||||
\(708\) | 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 | \(-0.382062\pi\) | ||||
0.362093 | + | 0.932142i | \(0.382062\pi\) | |||||||
\(720\) | 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 | 0.787241 | − | 0.616645i | \(-0.211509\pi\) |
−0.616645 | + | 0.787241i | \(0.711509\pi\) | |||||||
\(744\) | 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 | −0.873935 | − | 0.486042i | \(-0.838440\pi\) |
0.486042 | + | 0.873935i | \(0.338440\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.137347 | 0.00498539 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 28.1860i | 1.02174i | 0.859657 | + | 0.510871i | \(0.170677\pi\) | ||||
−0.859657 | + | 0.510871i | \(0.829323\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.77797 | + | 9.56294i | −0.100569 | + | 0.346201i | ||||
\(764\) | 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 | \(-0.417586\pi\) | ||||
0.256029 | + | 0.966669i | \(0.417586\pi\) | |||||||
\(770\) | 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 | ||||||||
\(777\) | −4.71138 | + | 16.2186i | −0.169020 | + | 0.581838i | ||||
\(778\) | 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 | \(0.321350\pi\) | ||||
−0.532240 | + | 0.846593i | \(0.678650\pi\) | |||||||
\(812\) | 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 | \(-0.985697\pi\) |
−0.0449175 | − | 0.998991i | \(-0.514303\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −3.77895 | + | 3.77895i | −0.131407 | + | 0.131407i | −0.769751 | − | 0.638344i | \(-0.779620\pi\) |
0.638344 | + | 0.769751i | \(0.279620\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −17.2917 | −0.600564 | −0.300282 | − | 0.953850i | \(-0.597081\pi\) | ||||
−0.300282 | + | 0.953850i | \(0.597081\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.76596i | 0.0959501i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −12.0896 | − | 54.0699i | −0.418879 | − | 1.87341i | ||||
\(834\) | 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 | \(-0.575052\pi\) | ||||
−0.233603 | + | 0.972332i | \(0.575052\pi\) | |||||||
\(840\) | 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 | ||||||||
\(847\) | 4.05970 | + | 1.17931i | 0.139493 | + | 0.0405217i | ||||
\(848\) | 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 | \(-0.539122\pi\) | ||||
−0.122597 | + | 0.992457i | \(0.539122\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.15929 | − | 7.56517i | −0.141748 | − | 0.257820i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 20.2042 | + | 20.2042i | 0.687758 | + | 0.687758i | 0.961736 | − | 0.273978i | \(-0.0883397\pi\) |
−0.273978 | + | 0.961736i | \(0.588340\pi\) | |||||||
\(864\) | 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 | −0.395038 | − | 0.918665i | \(-0.629269\pi\) |
0.918665 | + | 0.395038i | \(0.129269\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 5.33191i | − | 0.179841i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 35.4110i | − | 1.19303i | −0.802603 | − | 0.596513i | \(-0.796552\pi\) | ||
0.802603 | − | 0.596513i | \(-0.203448\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −29.1344 | − | 29.1344i | −0.980449 | − | 0.980449i | 0.0193631 | − | 0.999813i | \(-0.493836\pi\) |
−0.999813 | + | 0.0193631i | \(0.993836\pi\) | |||||||
\(884\) | 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 | ||||||||
\(903\) | 14.4264 | + | 4.19078i | 0.480082 | + | 0.139461i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −12.7400 | + | 12.7400i | −0.423024 | + | 0.423024i | −0.886244 | − | 0.463220i | \(-0.846694\pi\) |
0.463220 | + | 0.886244i | \(0.346694\pi\) | |||||||
\(908\) | 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 | ||||||||
\(917\) | −10.2041 | + | 35.1268i | −0.336969 | + | 1.15999i | ||||
\(918\) | 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 | \(-0.741260\pi\) | ||||
−0.687427 | + | 0.726254i | \(0.741260\pi\) | |||||||
\(930\) | 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 | \(-0.935051\pi\) | ||
0.979256 | − | 0.202629i | \(-0.0649486\pi\) | |||||||
\(942\) | 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 | \(0.522192\pi\) |
−0.997571 | + | 0.0696622i | \(0.977808\pi\) | |||||||
\(948\) | 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 | 0.950495 | − | 0.310739i | \(-0.100576\pi\) |
−0.310739 | + | 0.950495i | \(0.600576\pi\) | |||||||
\(954\) | 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 | −0.719228 | − | 0.694774i | \(-0.755504\pi\) |
0.694774 | + | 0.719228i | \(0.255504\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −16.4693 | −0.529070 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 35.7520i | − | 1.14733i | −0.819088 | − | 0.573667i | \(-0.805520\pi\) | ||
0.819088 | − | 0.573667i | \(-0.194480\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −19.2039 | − | 5.57859i | −0.615647 | − | 0.178841i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −22.3370 | + | 22.3370i | −0.714625 | + | 0.714625i | −0.967499 | − | 0.252874i | \(-0.918624\pi\) |
0.252874 | + | 0.967499i | \(0.418624\pi\) | |||||||
\(978\) | 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 | ||||||||
\(987\) | 7.15910 | + | 2.07967i | 0.227877 | + | 0.0661966i | ||||
\(988\) | 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.993.8 | yes | 32 | |
5.2 | odd | 4 | inner | 1400.2.x.c.657.10 | yes | 32 | |
5.3 | odd | 4 | inner | 1400.2.x.c.657.7 | ✓ | 32 | |
5.4 | even | 2 | inner | 1400.2.x.c.993.9 | yes | 32 | |
7.6 | odd | 2 | inner | 1400.2.x.c.993.10 | yes | 32 | |
35.13 | even | 4 | inner | 1400.2.x.c.657.9 | yes | 32 | |
35.27 | even | 4 | inner | 1400.2.x.c.657.8 | yes | 32 | |
35.34 | odd | 2 | inner | 1400.2.x.c.993.7 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1400.2.x.c.657.7 | ✓ | 32 | 5.3 | odd | 4 | inner | |
1400.2.x.c.657.8 | yes | 32 | 35.27 | even | 4 | inner | |
1400.2.x.c.657.9 | yes | 32 | 35.13 | even | 4 | inner | |
1400.2.x.c.657.10 | yes | 32 | 5.2 | odd | 4 | inner | |
1400.2.x.c.993.7 | yes | 32 | 35.34 | odd | 2 | inner | |
1400.2.x.c.993.8 | yes | 32 | 1.1 | even | 1 | trivial | |
1400.2.x.c.993.9 | yes | 32 | 5.4 | even | 2 | inner | |
1400.2.x.c.993.10 | yes | 32 | 7.6 | odd | 2 | inner |