Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1440,2,Mod(17,1440)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1440, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 2, 2, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1440.17");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1440 = 2^{5} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1440.bj (of order \(4\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(11.4984578911\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 360) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 17.22 | ||
Character | \(\chi\) | \(=\) | 1440.17 |
Dual form | 1440.2.bj.a.593.22 |
$q$-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 \(\left(\mathbb{Z}/1440\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(641\) | \(901\) | \(991\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.03368 | − | 0.929591i | 0.909490 | − | 0.415726i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.49469 | + | 2.49469i | 0.942904 | + | 0.942904i | 0.998456 | − | 0.0555517i | \(-0.0176918\pi\) |
−0.0555517 | + | 0.998456i | \(0.517692\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.92878 | 1.18457 | 0.592286 | − | 0.805728i | \(-0.298226\pi\) | ||||
0.592286 | + | 0.805728i | \(0.298226\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.55591 | − | 4.55591i | −1.26358 | − | 1.26358i | −0.949345 | − | 0.314237i | \(-0.898251\pi\) |
−0.314237 | − | 0.949345i | \(-0.601749\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.88566 | − | 1.88566i | 0.457341 | − | 0.457341i | −0.440441 | − | 0.897782i | \(-0.645178\pi\) |
0.897782 | + | 0.440441i | \(0.145178\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.61555 | 1.05888 | 0.529440 | − | 0.848347i | \(-0.322402\pi\) | ||||
0.529440 | + | 0.848347i | \(0.322402\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.741221 | + | 0.741221i | 0.154555 | + | 0.154555i | 0.780149 | − | 0.625594i | \(-0.215143\pi\) |
−0.625594 | + | 0.780149i | \(0.715143\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.27172 | − | 3.78098i | 0.654344 | − | 0.756197i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.35885i | 0.809418i | 0.914446 | + | 0.404709i | \(0.132627\pi\) | ||||
−0.914446 | + | 0.404709i | \(0.867373\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.67119 | −1.73700 | −0.868499 | − | 0.495691i | \(-0.834915\pi\) | ||||
−0.868499 | + | 0.495691i | \(0.834915\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 7.39245 | + | 2.75436i | 1.24955 | + | 0.465572i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.39704 | − | 5.39704i | 0.887267 | − | 0.887267i | −0.106992 | − | 0.994260i | \(-0.534122\pi\) |
0.994260 | + | 0.106992i | \(0.0341221\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.33584i | 0.989492i | 0.869038 | + | 0.494746i | \(0.164739\pi\) | ||||
−0.869038 | + | 0.494746i | \(0.835261\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.206110 | + | 0.206110i | 0.0314315 | + | 0.0314315i | 0.722648 | − | 0.691216i | \(-0.242925\pi\) |
−0.691216 | + | 0.722648i | \(0.742925\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.48081 | + | 3.48081i | −0.507729 | + | 0.507729i | −0.913829 | − | 0.406100i | \(-0.866888\pi\) |
0.406100 | + | 0.913829i | \(0.366888\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.44695i | 0.778136i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.01974 | − | 1.01974i | 0.140073 | − | 0.140073i | −0.633593 | − | 0.773666i | \(-0.718421\pi\) |
0.773666 | + | 0.633593i | \(0.218421\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 7.98989 | − | 3.65216i | 1.07736 | − | 0.492457i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 0.531064i | − | 0.0691386i | −0.999402 | − | 0.0345693i | \(-0.988994\pi\) | ||
0.999402 | − | 0.0345693i | \(-0.0110059\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 3.00356i | − | 0.384566i | −0.981340 | − | 0.192283i | \(-0.938411\pi\) | ||
0.981340 | − | 0.192283i | \(-0.0615892\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −13.5004 | − | 5.03014i | −1.67452 | − | 0.623912i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.28660 | + | 1.28660i | −0.157183 | + | 0.157183i | −0.781317 | − | 0.624134i | \(-0.785452\pi\) |
0.624134 | + | 0.781317i | \(0.285452\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.61692i | 0.903962i | 0.892028 | + | 0.451981i | \(0.149282\pi\) | ||||
−0.892028 | + | 0.451981i | \(0.850718\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.509262 | + | 0.509262i | −0.0596047 | + | 0.0596047i | −0.736281 | − | 0.676676i | \(-0.763420\pi\) |
0.676676 | + | 0.736281i | \(0.263420\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 9.80109 | + | 9.80109i | 1.11694 | + | 1.11694i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.31920i | 0.148422i | 0.997243 | + | 0.0742111i | \(0.0236439\pi\) | ||||
−0.997243 | + | 0.0742111i | \(0.976356\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 9.85533 | − | 9.85533i | 1.08176 | − | 1.08176i | 0.0854172 | − | 0.996345i | \(-0.472778\pi\) |
0.996345 | − | 0.0854172i | \(-0.0272223\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.08194 | − | 5.58774i | 0.225819 | − | 0.606075i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.91798 | 0.309306 | 0.154653 | − | 0.987969i | \(-0.450574\pi\) | ||||
0.154653 | + | 0.987969i | \(0.450574\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 22.7312i | − | 2.38287i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 9.38656 | − | 4.29057i | 0.963041 | − | 0.440204i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.11369 | − | 8.11369i | −0.823820 | − | 0.823820i | 0.162834 | − | 0.986654i | \(-0.447937\pi\) |
−0.986654 | + | 0.162834i | \(0.947937\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 11.0269 | 1.09721 | 0.548607 | − | 0.836080i | \(-0.315158\pi\) | ||||
0.548607 | + | 0.836080i | \(0.315158\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.89128 | − | 2.89128i | 0.284887 | − | 0.284887i | −0.550168 | − | 0.835054i | \(-0.685436\pi\) |
0.835054 | + | 0.550168i | \(0.185436\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.23891 | + | 5.23891i | 0.506465 | + | 0.506465i | 0.913439 | − | 0.406975i | \(-0.133416\pi\) |
−0.406975 | + | 0.913439i | \(0.633416\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.31464 | −0.509050 | −0.254525 | − | 0.967066i | \(-0.581919\pi\) | ||||
−0.254525 | + | 0.967066i | \(0.581919\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.3559 | + | 10.3559i | 0.974204 | + | 0.974204i | 0.999676 | − | 0.0254720i | \(-0.00810886\pi\) |
−0.0254720 | + | 0.999676i | \(0.508109\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.19644 | + | 0.818375i | 0.204819 | + | 0.0763138i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 9.40829 | 0.862457 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.43532 | 0.403211 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3.13887 | − | 10.7307i | 0.280749 | − | 0.959781i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.10872 | + | 1.10872i | 0.0983826 | + | 0.0983826i | 0.754585 | − | 0.656202i | \(-0.227838\pi\) |
−0.656202 | + | 0.754585i | \(0.727838\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.996979 | 0.0871065 | 0.0435532 | − | 0.999051i | \(-0.486132\pi\) | ||||
0.0435532 | + | 0.999051i | \(0.486132\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 11.5144 | + | 11.5144i | 0.998422 | + | 0.998422i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.03232 | + | 1.03232i | −0.0881970 | + | 0.0881970i | −0.749829 | − | 0.661632i | \(-0.769864\pi\) |
0.661632 | + | 0.749829i | \(0.269864\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −16.9830 | −1.44048 | −0.720239 | − | 0.693726i | \(-0.755968\pi\) | ||||
−0.720239 | + | 0.693726i | \(0.755968\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −17.8992 | − | 17.8992i | −1.49680 | − | 1.49680i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.05194 | + | 8.86451i | 0.336496 | + | 0.736157i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 6.48772i | − | 0.531495i | −0.964043 | − | 0.265747i | \(-0.914381\pi\) | ||
0.964043 | − | 0.265747i | \(-0.0856187\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.21210 | −0.342776 | −0.171388 | − | 0.985204i | \(-0.554825\pi\) | ||||
−0.171388 | + | 0.985204i | \(0.554825\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −19.6681 | + | 8.99025i | −1.57978 | + | 0.722114i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.0368875 | − | 0.0368875i | 0.00294395 | − | 0.00294395i | −0.705633 | − | 0.708577i | \(-0.749337\pi\) |
0.708577 | + | 0.705633i | \(0.249337\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.69823i | 0.291461i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.33256 | + | 1.33256i | 0.104374 | + | 0.104374i | 0.757365 | − | 0.652991i | \(-0.226486\pi\) |
−0.652991 | + | 0.757365i | \(0.726486\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −15.0291 | + | 15.0291i | −1.16299 | + | 1.16299i | −0.179169 | + | 0.983818i | \(0.557341\pi\) |
−0.983818 | + | 0.179169i | \(0.942659\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 28.5126i | 2.19328i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2.16963 | + | 2.16963i | −0.164954 | + | 0.164954i | −0.784757 | − | 0.619804i | \(-0.787212\pi\) |
0.619804 | + | 0.784757i | \(0.287212\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 17.5943 | − | 1.27045i | 1.33000 | − | 0.0960371i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 14.2973i | 1.06863i | 0.845285 | + | 0.534316i | \(0.179431\pi\) | ||||
−0.845285 | + | 0.534316i | \(0.820569\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.0562i | 0.821800i | 0.911680 | + | 0.410900i | \(0.134785\pi\) | ||||
−0.911680 | + | 0.410900i | \(0.865215\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.95882 | − | 15.9929i | 0.438101 | − | 1.17582i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.40836 | − | 7.40836i | 0.541753 | − | 0.541753i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 12.7129i | − | 0.919873i | −0.887952 | − | 0.459937i | \(-0.847872\pi\) | ||
0.887952 | − | 0.459937i | \(-0.152128\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 16.5832 | − | 16.5832i | 1.19368 | − | 1.19368i | 0.217659 | − | 0.976025i | \(-0.430158\pi\) |
0.976025 | − | 0.217659i | \(-0.0698420\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −9.96244 | − | 9.96244i | −0.709794 | − | 0.709794i | 0.256698 | − | 0.966492i | \(-0.417366\pi\) |
−0.966492 | + | 0.256698i | \(0.917366\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 15.6722i | 1.11097i | 0.831525 | + | 0.555487i | \(0.187468\pi\) | ||||
−0.831525 | + | 0.555487i | \(0.812532\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −10.8740 | + | 10.8740i | −0.763203 | + | 0.763203i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.88974 | + | 12.8851i | 0.411357 | + | 0.899933i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 18.1335 | 1.25432 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 22.1294i | 1.52345i | 0.647901 | + | 0.761725i | \(0.275647\pi\) | ||||
−0.647901 | + | 0.761725i | \(0.724353\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.610761 | + | 0.227564i | 0.0416535 | + | 0.0155198i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −24.1266 | − | 24.1266i | −1.63782 | − | 1.63782i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −17.1818 | −1.15577 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.17650 | − | 3.17650i | 0.212714 | − | 0.212714i | −0.592705 | − | 0.805420i | \(-0.701940\pi\) |
0.805420 | + | 0.592705i | \(0.201940\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −18.4920 | − | 18.4920i | −1.22735 | − | 1.22735i | −0.964961 | − | 0.262393i | \(-0.915488\pi\) |
−0.262393 | − | 0.964961i | \(-0.584512\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −19.2316 | −1.27086 | −0.635428 | − | 0.772160i | \(-0.719176\pi\) | ||||
−0.635428 | + | 0.772160i | \(0.719176\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −13.7302 | − | 13.7302i | −0.899495 | − | 0.899495i | 0.0958959 | − | 0.995391i | \(-0.469428\pi\) |
−0.995391 | + | 0.0958959i | \(0.969428\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.84313 | + | 10.3146i | −0.250698 | + | 0.672850i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 26.7732 | 1.73182 | 0.865908 | − | 0.500203i | \(-0.166741\pi\) | ||||
0.865908 | + | 0.500203i | \(0.166741\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −17.6357 | −1.13601 | −0.568007 | − | 0.823023i | \(-0.692286\pi\) | ||||
−0.568007 | + | 0.823023i | \(0.692286\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5.06344 | + | 11.0774i | 0.323491 | + | 0.707707i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −21.0280 | − | 21.0280i | −1.33798 | − | 1.33798i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −13.0522 | −0.823846 | −0.411923 | − | 0.911219i | \(-0.635143\pi\) | ||||
−0.411923 | + | 0.911219i | \(0.635143\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.91209 | + | 2.91209i | 0.183082 | + | 0.183082i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −9.03127 | + | 9.03127i | −0.563355 | + | 0.563355i | −0.930259 | − | 0.366904i | \(-0.880418\pi\) |
0.366904 | + | 0.930259i | \(0.380418\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 26.9279 | 1.67322 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.83442 | − | 2.83442i | −0.174778 | − | 0.174778i | 0.614297 | − | 0.789075i | \(-0.289440\pi\) |
−0.789075 | + | 0.614297i | \(0.789440\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.12589 | − | 3.02178i | 0.0691629 | − | 0.185627i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 9.89975i | − | 0.603599i | −0.953371 | − | 0.301799i | \(-0.902413\pi\) | ||
0.953371 | − | 0.301799i | \(-0.0975873\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −16.6235 | −1.00981 | −0.504904 | − | 0.863176i | \(-0.668472\pi\) | ||||
−0.504904 | + | 0.863176i | \(0.668472\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 12.8539 | − | 14.8547i | 0.775118 | − | 0.895769i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.42695 | − | 6.42695i | 0.386158 | − | 0.386158i | −0.487156 | − | 0.873315i | \(-0.661966\pi\) |
0.873315 | + | 0.487156i | \(0.161966\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 27.0270i | 1.61230i | 0.591714 | + | 0.806148i | \(0.298451\pi\) | ||||
−0.591714 | + | 0.806148i | \(0.701549\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −18.1481 | − | 18.1481i | −1.07879 | − | 1.07879i | −0.996618 | − | 0.0821722i | \(-0.973814\pi\) |
−0.0821722 | − | 0.996618i | \(-0.526186\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −15.8060 | + | 15.8060i | −0.932996 | + | 0.932996i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 9.88854i | 0.581679i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −11.4905 | + | 11.4905i | −0.671281 | + | 0.671281i | −0.958011 | − | 0.286730i | \(-0.907432\pi\) |
0.286730 | + | 0.958011i | \(0.407432\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.493672 | − | 1.08001i | −0.0287427 | − | 0.0628809i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 6.75387i | − | 0.390586i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.02836i | 0.0592738i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.79208 | − | 6.10828i | −0.159874 | − | 0.349759i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −17.8635 | + | 17.8635i | −1.01953 | + | 1.01953i | −0.0197205 | + | 0.999806i | \(0.506278\pi\) |
−0.999806 | + | 0.0197205i | \(0.993722\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 9.93768i | − | 0.563514i | −0.959486 | − | 0.281757i | \(-0.909083\pi\) | ||
0.959486 | − | 0.281757i | \(-0.0909173\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.20616 | − | 5.20616i | 0.294269 | − | 0.294269i | −0.544495 | − | 0.838764i | \(-0.683279\pi\) |
0.838764 | + | 0.544495i | \(0.183279\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −13.2883 | − | 13.2883i | −0.746346 | − | 0.746346i | 0.227445 | − | 0.973791i | \(-0.426963\pi\) |
−0.973791 | + | 0.227445i | \(0.926963\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 17.1250i | 0.958813i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8.70338 | − | 8.70338i | 0.484269 | − | 0.484269i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −32.1315 | + | 2.32015i | −1.78233 | + | 0.128699i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −17.3671 | −0.957479 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.60834i | 0.473157i | 0.971612 | + | 0.236579i | \(0.0760261\pi\) | ||||
−0.971612 | + | 0.236579i | \(0.923974\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.42052 | + | 3.81255i | −0.0776114 | + | 0.208302i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.29928 | + | 1.29928i | 0.0707764 | + | 0.0707764i | 0.741609 | − | 0.670832i | \(-0.234063\pi\) |
−0.670832 | + | 0.741609i | \(0.734063\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −37.9960 | −2.05760 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.87437 | − | 3.87437i | 0.209196 | − | 0.209196i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −18.3626 | − | 18.3626i | −0.985756 | − | 0.985756i | 0.0141438 | − | 0.999900i | \(-0.495498\pi\) |
−0.999900 | + | 0.0141438i | \(0.995498\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 31.1787 | 1.66896 | 0.834478 | − | 0.551041i | \(-0.185769\pi\) | ||||
0.834478 | + | 0.551041i | \(0.185769\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −9.04629 | − | 9.04629i | −0.481485 | − | 0.481485i | 0.424120 | − | 0.905606i | \(-0.360583\pi\) |
−0.905606 | + | 0.424120i | \(0.860583\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7.08062 | + | 15.4904i | 0.375800 | + | 0.822144i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 13.1073 | 0.691776 | 0.345888 | − | 0.938276i | \(-0.387578\pi\) | ||||
0.345888 | + | 0.938276i | \(0.387578\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.30330 | 0.121226 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.562272 | + | 1.50908i | −0.0294307 | + | 0.0789890i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.44746 | − | 3.44746i | −0.179956 | − | 0.179956i | 0.611381 | − | 0.791337i | \(-0.290614\pi\) |
−0.791337 | + | 0.611381i | \(0.790614\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.08789 | 0.264150 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.24984 | − | 7.24984i | −0.375382 | − | 0.375382i | 0.494051 | − | 0.869433i | \(-0.335516\pi\) |
−0.869433 | + | 0.494051i | \(0.835516\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 19.8585 | − | 19.8585i | 1.02277 | − | 1.02277i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −29.1664 | −1.49818 | −0.749088 | − | 0.662470i | \(-0.769508\pi\) | ||||
−0.749088 | + | 0.662470i | \(0.769508\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 12.2895 | + | 12.2895i | 0.627965 | + | 0.627965i | 0.947556 | − | 0.319591i | \(-0.103545\pi\) |
−0.319591 | + | 0.947556i | \(0.603545\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 29.0433 | + | 10.8213i | 1.48018 | + | 0.551504i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 31.4290i | 1.59351i | 0.604301 | + | 0.796756i | \(0.293452\pi\) | ||||
−0.604301 | + | 0.796756i | \(0.706548\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.79539 | 0.141369 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.22632 | + | 2.68284i | 0.0617029 | + | 0.134988i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −14.9362 | + | 14.9362i | −0.749627 | + | 0.749627i | −0.974409 | − | 0.224782i | \(-0.927833\pi\) |
0.224782 | + | 0.974409i | \(0.427833\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 27.0477i | − | 1.35070i | −0.737499 | − | 0.675349i | \(-0.763993\pi\) | ||
0.737499 | − | 0.675349i | \(-0.236007\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 44.0611 | + | 44.0611i | 2.19484 | + | 2.19484i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 21.2038 | − | 21.2038i | 1.05103 | − | 1.05103i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.66540i | 0.230689i | 0.993326 | + | 0.115345i | \(0.0367973\pi\) | ||||
−0.993326 | + | 0.115345i | \(0.963203\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.32484 | − | 1.32484i | 0.0651911 | − | 0.0651911i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 10.8812 | − | 29.2040i | 0.534136 | − | 1.43357i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 2.43646i | − | 0.119029i | −0.998227 | − | 0.0595144i | \(-0.981045\pi\) | ||
0.998227 | − | 0.0595144i | \(-0.0189552\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 9.62136i | − | 0.468916i | −0.972126 | − | 0.234458i | \(-0.924668\pi\) | ||
0.972126 | − | 0.234458i | \(-0.0753316\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.960298 | − | 13.2990i | −0.0465813 | − | 0.645098i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.49294 | − | 7.49294i | 0.362609 | − | 0.362609i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 26.4447i | 1.27380i | 0.770948 | + | 0.636898i | \(0.219783\pi\) | ||||
−0.770948 | + | 0.636898i | \(0.780217\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.22850 | − | 5.22850i | 0.251266 | − | 0.251266i | −0.570224 | − | 0.821490i | \(-0.693143\pi\) |
0.821490 | + | 0.570224i | \(0.193143\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.42114 | + | 3.42114i | 0.163655 | + | 0.163655i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 37.3742i | 1.78377i | 0.452258 | + | 0.891887i | \(0.350619\pi\) | ||||
−0.452258 | + | 0.891887i | \(0.649381\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −18.0711 | + | 18.0711i | −0.858585 | + | 0.858585i | −0.991171 | − | 0.132587i | \(-0.957672\pi\) |
0.132587 | + | 0.991171i | \(0.457672\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5.93425 | − | 2.71253i | 0.281310 | − | 0.128586i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 24.4570 | 1.15420 | 0.577098 | − | 0.816675i | \(-0.304185\pi\) | ||||
0.577098 | + | 0.816675i | \(0.304185\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 24.8921i | 1.17212i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −21.1307 | − | 46.2279i | −0.990621 | − | 2.16720i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.76322 | + | 5.76322i | 0.269592 | + | 0.269592i | 0.828936 | − | 0.559344i | \(-0.188947\pi\) |
−0.559344 | + | 0.828936i | \(0.688947\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −10.6204 | −0.494639 | −0.247320 | − | 0.968934i | \(-0.579550\pi\) | ||||
−0.247320 | + | 0.968934i | \(0.579550\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13.7984 | + | 13.7984i | −0.641268 | + | 0.641268i | −0.950867 | − | 0.309599i | \(-0.899805\pi\) |
0.309599 | + | 0.950867i | \(0.399805\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 11.6749 | + | 11.6749i | 0.540248 | + | 0.540248i | 0.923602 | − | 0.383354i | \(-0.125231\pi\) |
−0.383354 | + | 0.923602i | \(0.625231\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.41933 | −0.296417 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.809762 | + | 0.809762i | 0.0372329 | + | 0.0372329i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 15.1008 | − | 17.4513i | 0.692872 | − | 0.800721i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5.10716 | −0.233352 | −0.116676 | − | 0.993170i | \(-0.537224\pi\) | ||||
−0.116676 | + | 0.993170i | \(0.537224\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −49.1768 | −2.24227 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −24.0431 | − | 8.95824i | −1.09174 | − | 0.406773i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3.80542 | − | 3.80542i | −0.172440 | − | 0.172440i | 0.615611 | − | 0.788050i | \(-0.288909\pi\) |
−0.788050 | + | 0.615611i | \(0.788909\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −19.3774 | −0.874492 | −0.437246 | − | 0.899342i | \(-0.644046\pi\) | ||||
−0.437246 | + | 0.899342i | \(0.644046\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.21932 | + | 8.21932i | 0.370180 | + | 0.370180i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −19.0018 | + | 19.0018i | −0.852349 | + | 0.852349i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −21.5723 | −0.965707 | −0.482853 | − | 0.875701i | \(-0.660400\pi\) | ||||
−0.482853 | + | 0.875701i | \(0.660400\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0.650945 | + | 0.650945i | 0.0290242 | + | 0.0290242i | 0.721470 | − | 0.692446i | \(-0.243467\pi\) |
−0.692446 | + | 0.721470i | \(0.743467\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 22.4251 | − | 10.2505i | 0.997906 | − | 0.456140i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 9.29371i | − | 0.411937i | −0.978559 | − | 0.205968i | \(-0.933966\pi\) | ||
0.978559 | − | 0.205968i | \(-0.0660344\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.54090 | −0.112403 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.19224 | − | 8.56766i | 0.140667 | − | 0.377536i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −13.6753 | + | 13.6753i | −0.601441 | + | 0.601441i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 37.4945i | 1.64266i | 0.570451 | + | 0.821331i | \(0.306768\pi\) | ||||
−0.570451 | + | 0.821331i | \(0.693232\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −18.0635 | − | 18.0635i | −0.789861 | − | 0.789861i | 0.191610 | − | 0.981471i | \(-0.438629\pi\) |
−0.981471 | + | 0.191610i | \(0.938629\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −18.2366 | + | 18.2366i | −0.794400 | + | 0.794400i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 21.9012i | − | 0.952225i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 28.8655 | − | 28.8655i | 1.25030 | − | 1.25030i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 15.5243 | + | 5.78423i | 0.671175 | + | 0.250074i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 21.3999i | 0.921758i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 29.6103i | − | 1.27305i | −0.771258 | − | 0.636523i | \(-0.780372\pi\) | ||
0.771258 | − | 0.636523i | \(-0.219628\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −10.8083 | + | 4.94044i | −0.462976 | + | 0.211625i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 13.8891 | − | 13.8891i | 0.593855 | − | 0.593855i | −0.344816 | − | 0.938670i | \(-0.612059\pi\) |
0.938670 | + | 0.344816i | \(0.112059\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 20.1185i | 0.857076i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.29101 | + | 3.29101i | −0.139948 | + | 0.139948i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 16.0818 | + | 16.0818i | 0.681408 | + | 0.681408i | 0.960317 | − | 0.278910i | \(-0.0899730\pi\) |
−0.278910 | + | 0.960317i | \(0.589973\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 1.87804i | − | 0.0794326i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 11.6731 | − | 11.6731i | 0.491962 | − | 0.491962i | −0.416962 | − | 0.908924i | \(-0.636905\pi\) |
0.908924 | + | 0.416962i | \(0.136905\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 30.6874 | + | 11.4339i | 1.29103 | + | 0.481027i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 26.5009 | 1.11098 | 0.555488 | − | 0.831524i | \(-0.312531\pi\) | ||||
0.555488 | + | 0.831524i | \(0.312531\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 42.2873i | − | 1.76967i | −0.465904 | − | 0.884835i | \(-0.654271\pi\) | ||
0.465904 | − | 0.884835i | \(-0.345729\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5.22761 | − | 0.377476i | 0.218006 | − | 0.0157418i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10.2682 | + | 10.2682i | 0.427473 | + | 0.427473i | 0.887767 | − | 0.460294i | \(-0.152256\pi\) |
−0.460294 | + | 0.887767i | \(0.652256\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 49.1720 | 2.04000 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.00635 | − | 4.00635i | 0.165926 | − | 0.165926i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 18.7596 | + | 18.7596i | 0.774290 | + | 0.774290i | 0.978853 | − | 0.204563i | \(-0.0655773\pi\) |
−0.204563 | + | 0.978853i | \(0.565577\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −44.6379 | −1.83927 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.79755 | − | 1.79755i | −0.0738164 | − | 0.0738164i | 0.669235 | − | 0.743051i | \(-0.266622\pi\) |
−0.743051 | + | 0.669235i | \(0.766622\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 19.1335 | − | 8.74586i | 0.784396 | − | 0.358545i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −34.7082 | −1.41814 | −0.709069 | − | 0.705139i | \(-0.750885\pi\) | ||||
−0.709069 | + | 0.705139i | \(0.750885\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.66540 | −0.353469 | −0.176735 | − | 0.984259i | \(-0.556553\pi\) | ||||
−0.176735 | + | 0.984259i | \(0.556553\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 9.02002 | − | 4.12303i | 0.366716 | − | 0.167625i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.31702 | + | 5.31702i | 0.215811 | + | 0.215811i | 0.806731 | − | 0.590919i | \(-0.201235\pi\) |
−0.590919 | + | 0.806731i | \(0.701235\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 31.7165 | 1.28311 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −0.848748 | − | 0.848748i | −0.0342806 | − | 0.0342806i | 0.689759 | − | 0.724039i | \(-0.257717\pi\) |
−0.724039 | + | 0.689759i | \(0.757717\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −16.6187 | + | 16.6187i | −0.669043 | + | 0.669043i | −0.957494 | − | 0.288452i | \(-0.906859\pi\) |
0.288452 | + | 0.957494i | \(0.406859\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6.21940 | 0.249979 | 0.124989 | − | 0.992158i | \(-0.460110\pi\) | ||||
0.124989 | + | 0.992158i | \(0.460110\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 7.27946 | + | 7.27946i | 0.291646 | + | 0.291646i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −3.59168 | − | 24.7407i | −0.143667 | − | 0.989626i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 20.3540i | − | 0.811567i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12.0019 | −0.477790 | −0.238895 | − | 0.971045i | \(-0.576785\pi\) | ||||
−0.238895 | + | 0.971045i | \(0.576785\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3.28543 | + | 1.22412i | 0.130378 | + | 0.0485778i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 24.8158 | − | 24.8158i | 0.983239 | − | 0.983239i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 6.27061i | − | 0.247674i | −0.992303 | − | 0.123837i | \(-0.960480\pi\) | ||
0.992303 | − | 0.123837i | \(-0.0395200\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −15.3358 | − | 15.3358i | −0.604787 | − | 0.604787i | 0.336792 | − | 0.941579i | \(-0.390658\pi\) |
−0.941579 | + | 0.336792i | \(0.890658\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 28.9583 | − | 28.9583i | 1.13847 | − | 1.13847i | 0.149741 | − | 0.988725i | \(-0.452156\pi\) |
0.988725 | − | 0.149741i | \(-0.0478441\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 2.08643i | − | 0.0818997i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.21463 | − | 2.21463i | 0.0866651 | − | 0.0866651i | −0.662445 | − | 0.749110i | \(-0.730481\pi\) |
0.749110 | + | 0.662445i | \(0.230481\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.02754 | − | 0.926783i | 0.0792225 | − | 0.0362124i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 37.2920i | − | 1.45269i | −0.687330 | − | 0.726345i | \(-0.741218\pi\) | ||
0.687330 | − | 0.726345i | \(-0.258782\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 6.19442i | − | 0.240935i | −0.992717 | − | 0.120467i | \(-0.961561\pi\) | ||
0.992717 | − | 0.120467i | \(-0.0384393\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 34.1202 | + | 12.7129i | 1.32312 | + | 0.492985i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.23087 | + | 3.23087i | −0.125100 | + | 0.125100i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 11.8003i | − | 0.455546i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −27.8727 | + | 27.8727i | −1.07441 | + | 1.07441i | −0.0774133 | + | 0.996999i | \(0.524666\pi\) |
−0.996999 | + | 0.0774133i | \(0.975334\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 10.0200 | + | 10.0200i | 0.385098 | + | 0.385098i | 0.872935 | − | 0.487837i | \(-0.162214\pi\) |
−0.487837 | + | 0.872935i | \(0.662214\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 40.4823i | − | 1.55357i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −11.5229 | + | 11.5229i | −0.440911 | + | 0.440911i | −0.892318 | − | 0.451407i | \(-0.850922\pi\) |
0.451407 | + | 0.892318i | \(0.350922\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.13977 | + | 3.05904i | −0.0435485 | + | 0.116880i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −9.29173 | −0.353987 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 18.3907i | − | 0.699614i | −0.936822 | − | 0.349807i | \(-0.886247\pi\) | ||
0.936822 | − | 0.349807i | \(-0.113753\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −34.5380 | + | 15.7872i | −1.31010 | + | 0.598844i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 11.9473 | + | 11.9473i | 0.452535 | + | 0.452535i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 52.0764 | 1.96690 | 0.983449 | − | 0.181186i | \(-0.0579937\pi\) | ||||
0.983449 | + | 0.181186i | \(0.0579937\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 24.9103 | − | 24.9103i | 0.939509 | − | 0.939509i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 27.5086 | + | 27.5086i | 1.03457 | + | 1.03457i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 49.8546 | 1.87233 | 0.936165 | − | 0.351561i | \(-0.114349\pi\) | ||||
0.936165 | + | 0.351561i | \(0.114349\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −7.16849 | − | 7.16849i | −0.268462 | − | 0.268462i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −53.0401 | − | 19.7623i | −1.98359 | − | 0.739068i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 21.3548 | 0.796400 | 0.398200 | − | 0.917299i | \(-0.369635\pi\) | ||||
0.398200 | + | 0.917299i | \(0.369635\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 14.4257 | 0.537242 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 16.4807 | + | 14.2609i | 0.612079 | + | 0.529638i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −13.1166 | − | 13.1166i | −0.486469 | − | 0.486469i | 0.420721 | − | 0.907190i | \(-0.361777\pi\) |
−0.907190 | + | 0.420721i | \(0.861777\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.777309 | 0.0287498 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3.40526 | + | 3.40526i | 0.125776 | + | 0.125776i | 0.767193 | − | 0.641417i | \(-0.221653\pi\) |
−0.641417 | + | 0.767193i | \(0.721653\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5.05477 | + | 5.05477i | −0.186195 | + | 0.186195i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6.84745 | 0.251887 | 0.125944 | − | 0.992037i | \(-0.459804\pi\) | ||||
0.125944 | + | 0.992037i | \(0.459804\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 9.83167 | + | 9.83167i | 0.360689 | + | 0.360689i | 0.864067 | − | 0.503377i | \(-0.167909\pi\) |
−0.503377 | + | 0.864067i | \(0.667909\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.03092 | − | 13.1940i | −0.220956 | − | 0.483389i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 26.1389i | 0.955095i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 36.1038 | 1.31745 | 0.658723 | − | 0.752385i | \(-0.271097\pi\) | ||||
0.658723 | + | 0.752385i | \(0.271097\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −8.56606 | + | 3.91553i | −0.311751 | + | 0.142501i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 26.0495 | − | 26.0495i | 0.946785 | − | 0.946785i | −0.0518693 | − | 0.998654i | \(-0.516518\pi\) |
0.998654 | + | 0.0518693i | \(0.0165179\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 29.4006i | − | 1.06577i | −0.846188 | − | 0.532885i | \(-0.821108\pi\) | ||
0.846188 | − | 0.532885i | \(-0.178892\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −13.2584 | − | 13.2584i | −0.479986 | − | 0.479986i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.41948 | + | 2.41948i | −0.0873623 | + | 0.0873623i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 39.4234i | 1.42164i | 0.703372 | + | 0.710822i | \(0.251677\pi\) | ||||
−0.703372 | + | 0.710822i | \(0.748323\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.76896 | − | 2.76896i | 0.0995925 | − | 0.0995925i | −0.655555 | − | 0.755147i | \(-0.727565\pi\) |
0.755147 | + | 0.655555i | \(0.227565\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −31.6414 | + | 36.5666i | −1.13659 | + | 1.31351i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 29.2434i | 1.04775i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 29.9252i | 1.07081i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.0407272 | − | 0.109308i | 0.00145362 | − | 0.00390136i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 20.1445 | − | 20.1445i | 0.718072 | − | 0.718072i | −0.250138 | − | 0.968210i | \(-0.580476\pi\) |
0.968210 | + | 0.250138i | \(0.0804760\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 51.6696i | 1.83716i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −13.6839 | + | 13.6839i | −0.485931 | + | 0.485931i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −27.4953 | − | 27.4953i | −0.973933 | − | 0.973933i | 0.0257360 | − | 0.999669i | \(-0.491807\pi\) |
−0.999669 | + | 0.0257360i | \(0.991807\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 13.1273i | 0.464410i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.00078 | + | 2.00078i | −0.0706060 | + | 0.0706060i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.43784 | + | 7.52102i | 0.121168 | + | 0.265081i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −25.2679 | −0.888372 | −0.444186 | − | 0.895935i | \(-0.646507\pi\) | ||||
−0.444186 | + | 0.895935i | \(0.646507\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 25.9061i | − | 0.909687i | −0.890571 | − | 0.454844i | \(-0.849695\pi\) | ||
0.890571 | − | 0.454844i | \(-0.150305\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 3.94873 | + | 1.47126i | 0.138318 | + | 0.0515361i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.951312 | + | 0.951312i | 0.0332822 | + | 0.0332822i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −14.0659 | −0.490904 | −0.245452 | − | 0.969409i | \(-0.578936\pi\) | ||||
−0.245452 | + | 0.969409i | \(0.578936\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 18.9660 | − | 18.9660i | 0.661112 | − | 0.661112i | −0.294530 | − | 0.955642i | \(-0.595163\pi\) |
0.955642 | + | 0.294530i | \(0.0951632\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −5.96783 | − | 5.96783i | −0.207522 | − | 0.207522i | 0.595692 | − | 0.803213i | \(-0.296878\pi\) |
−0.803213 | + | 0.595692i | \(0.796878\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 8.93872 | 0.310454 | 0.155227 | − | 0.987879i | \(-0.450389\pi\) | ||||
0.155227 | + | 0.987879i | \(0.450389\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 10.2711 | + | 10.2711i | 0.355873 | + | 0.355873i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −16.5935 | + | 44.5354i | −0.574242 | + | 1.54121i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 7.98961 | 0.275832 | 0.137916 | − | 0.990444i | \(-0.455960\pi\) | ||||
0.137916 | + | 0.990444i | \(0.455960\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.0005 | 0.344843 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 26.5051 | + | 57.9855i | 0.911802 | + | 1.99476i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 11.0647 | + | 11.0647i | 0.380189 | + | 0.380189i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8.00079 | 0.274264 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −17.2928 | − | 17.2928i | −0.592094 | − | 0.592094i | 0.346103 | − | 0.938197i | \(-0.387505\pi\) |
−0.938197 | + | 0.346103i | \(0.887505\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −31.0209 | + | 31.0209i | −1.05965 | + | 1.05965i | −0.0615490 | + | 0.998104i | \(0.519604\pi\) |
−0.998104 | + | 0.0615490i | \(0.980396\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 30.7443 | 1.04898 | 0.524492 | − | 0.851416i | \(-0.324255\pi\) | ||||
0.524492 | + | 0.851416i | \(0.324255\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −26.9037 | − | 26.9037i | −0.915812 | − | 0.915812i | 0.0809092 | − | 0.996721i | \(-0.474218\pi\) |
−0.996721 | + | 0.0809092i | \(0.974218\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.39546 | + | 6.42919i | −0.0814482 | + | 0.218599i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.18287i | 0.175817i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 11.7233 | 0.397228 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 34.6002 | − | 18.9392i | 1.16970 | − | 0.640262i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −26.8633 | + | 26.8633i | −0.907111 | + | 0.907111i | −0.996038 | − | 0.0889274i | \(-0.971656\pi\) |
0.0889274 | + | 0.996038i | \(0.471656\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 5.85067i | 0.197114i | 0.995131 | + | 0.0985571i | \(0.0314227\pi\) | ||||
−0.995131 | + | 0.0985571i | \(0.968577\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 14.4524 | + | 14.4524i | 0.486362 | + | 0.486362i | 0.907156 | − | 0.420794i | \(-0.138249\pi\) |
−0.420794 | + | 0.907156i | \(0.638249\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 23.4185 | − | 23.4185i | 0.786317 | − | 0.786317i | −0.194571 | − | 0.980888i | \(-0.562332\pi\) |
0.980888 | + | 0.194571i | \(0.0623315\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5.53180i | 0.185531i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −16.0659 | + | 16.0659i | −0.537623 | + | 0.537623i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 13.2906 | + | 29.0762i | 0.444257 | + | 0.971909i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 42.1552i | − | 1.40596i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 3.84579i | − | 0.128122i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 10.2777 | + | 22.4848i | 0.341643 | + | 0.747419i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 15.8605 | − | 15.8605i | 0.526640 | − | 0.526640i | −0.392929 | − | 0.919569i | \(-0.628538\pi\) |
0.919569 | + | 0.392929i | \(0.128538\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 48.6371i | − | 1.61142i | −0.592310 | − | 0.805710i | \(-0.701784\pi\) | ||
0.592310 | − | 0.805710i | \(-0.298216\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 38.7194 | − | 38.7194i | 1.28143 | − | 1.28143i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.48715 | + | 2.48715i | 0.0821330 | + | 0.0821330i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 28.6171i | 0.943990i | 0.881601 | + | 0.471995i | \(0.156466\pi\) | ||||
−0.881601 | + | 0.471995i | \(0.843534\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 34.7020 | − | 34.7020i | 1.14223 | − | 1.14223i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.74851 | − | 38.0637i | −0.0903704 | − | 1.25153i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 27.8635 | 0.914171 | 0.457086 | − | 0.889423i | \(-0.348893\pi\) | ||||
0.457086 | + | 0.889423i | \(0.348893\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 25.1407i | 0.823953i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 8.17950 | − | 21.9530i | 0.267498 | − | 0.717939i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.53180 | − | 2.53180i | −0.0827105 | − | 0.0827105i | 0.664541 | − | 0.747252i | \(-0.268627\pi\) |
−0.747252 | + | 0.664541i | \(0.768627\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 28.8111 | 0.939216 | 0.469608 | − | 0.882875i | \(-0.344395\pi\) | ||||
0.469608 | + | 0.882875i | \(0.344395\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4.69626 | + | 4.69626i | −0.152931 | + | 0.152931i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 28.0862 | + | 28.0862i | 0.912678 | + | 0.912678i | 0.996482 | − | 0.0838038i | \(-0.0267069\pi\) |
−0.0838038 | + | 0.996482i | \(0.526707\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.64031 | 0.150631 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −23.3080 | − | 23.3080i | −0.755020 | − | 0.755020i | 0.220392 | − | 0.975411i | \(-0.429266\pi\) |
−0.975411 | + | 0.220392i | \(0.929266\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −11.8178 | − | 25.8540i | −0.382415 | − | 0.836616i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −5.15063 | −0.166323 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 62.5320 | 2.01716 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 18.3093 | − | 49.1405i | 0.589398 | − | 1.58189i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −27.4623 | − | 27.4623i | −0.883128 | − | 0.883128i | 0.110723 | − | 0.993851i | \(-0.464683\pi\) |
−0.993851 | + | 0.110723i | \(0.964683\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −41.1632 | −1.32099 | −0.660496 | − | 0.750830i | \(-0.729654\pi\) | ||||
−0.660496 | + | 0.750830i | \(0.729654\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −42.3673 | − | 42.3673i | −1.35823 | − | 1.35823i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 8.98437 | − | 8.98437i | 0.287435 | − | 0.287435i | −0.548630 | − | 0.836065i | \(-0.684850\pi\) |
0.836065 | + | 0.548630i | \(0.184850\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 11.4641 | 0.366395 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 37.2602 | + | 37.2602i | 1.18842 | + | 1.18842i | 0.977505 | + | 0.210910i | \(0.0676428\pi\) |
0.210910 | + | 0.977505i | \(0.432357\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −29.5214 | − | 10.9994i | −0.940631 | − | 0.350471i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.305546i | 0.00971581i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −20.4634 | −0.650040 | −0.325020 | − | 0.945707i | \(-0.605371\pi\) | ||||
−0.325020 | + | 0.945707i | \(0.605371\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 14.5687 | + | 31.8723i | 0.461860 | + | 1.01042i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −23.1571 | + | 23.1571i | −0.733392 | + | 0.733392i | −0.971290 | − | 0.237898i | \(-0.923542\pi\) |
0.237898 | + | 0.971290i | \(0.423542\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1440.2.bj.a.17.22 | 48 | ||
3.2 | odd | 2 | inner | 1440.2.bj.a.17.4 | 48 | ||
4.3 | odd | 2 | 360.2.x.a.197.9 | yes | 48 | ||
5.3 | odd | 4 | inner | 1440.2.bj.a.593.21 | 48 | ||
8.3 | odd | 2 | 360.2.x.a.197.4 | yes | 48 | ||
8.5 | even | 2 | inner | 1440.2.bj.a.17.3 | 48 | ||
12.11 | even | 2 | 360.2.x.a.197.16 | yes | 48 | ||
15.8 | even | 4 | inner | 1440.2.bj.a.593.3 | 48 | ||
20.3 | even | 4 | 360.2.x.a.53.21 | yes | 48 | ||
24.5 | odd | 2 | inner | 1440.2.bj.a.17.21 | 48 | ||
24.11 | even | 2 | 360.2.x.a.197.21 | yes | 48 | ||
40.3 | even | 4 | 360.2.x.a.53.16 | yes | 48 | ||
40.13 | odd | 4 | inner | 1440.2.bj.a.593.4 | 48 | ||
60.23 | odd | 4 | 360.2.x.a.53.4 | ✓ | 48 | ||
120.53 | even | 4 | inner | 1440.2.bj.a.593.22 | 48 | ||
120.83 | odd | 4 | 360.2.x.a.53.9 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
360.2.x.a.53.4 | ✓ | 48 | 60.23 | odd | 4 | ||
360.2.x.a.53.9 | yes | 48 | 120.83 | odd | 4 | ||
360.2.x.a.53.16 | yes | 48 | 40.3 | even | 4 | ||
360.2.x.a.53.21 | yes | 48 | 20.3 | even | 4 | ||
360.2.x.a.197.4 | yes | 48 | 8.3 | odd | 2 | ||
360.2.x.a.197.9 | yes | 48 | 4.3 | odd | 2 | ||
360.2.x.a.197.16 | yes | 48 | 12.11 | even | 2 | ||
360.2.x.a.197.21 | yes | 48 | 24.11 | even | 2 | ||
1440.2.bj.a.17.3 | 48 | 8.5 | even | 2 | inner | ||
1440.2.bj.a.17.4 | 48 | 3.2 | odd | 2 | inner | ||
1440.2.bj.a.17.21 | 48 | 24.5 | odd | 2 | inner | ||
1440.2.bj.a.17.22 | 48 | 1.1 | even | 1 | trivial | ||
1440.2.bj.a.593.3 | 48 | 15.8 | even | 4 | inner | ||
1440.2.bj.a.593.4 | 48 | 40.13 | odd | 4 | inner | ||
1440.2.bj.a.593.21 | 48 | 5.3 | odd | 4 | inner | ||
1440.2.bj.a.593.22 | 48 | 120.53 | even | 4 | inner |