Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2100,2,Mod(1349,2100)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2100, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2100.1349");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2100.bo (of order \(6\), 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: | \(16.7685844245\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1349.16 | ||
Character | \(\chi\) | \(=\) | 2100.1349 |
Dual form | 2100.2.bo.i.1949.16 |
$q$-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 \(\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times\).
\(n\) | \(701\) | \(1051\) | \(1177\) | \(1501\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) |
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 | ||||||||
\(3\) | 1.68420 | − | 0.404332i | 0.972371 | − | 0.233441i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.10133 | + | 1.60761i | −0.794228 | + | 0.607620i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.67303 | − | 1.36195i | 0.891010 | − | 0.453983i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.05856 | + | 1.18851i | −0.620679 | + | 0.358349i | −0.777133 | − | 0.629336i | \(-0.783327\pi\) |
0.156455 | + | 0.987685i | \(0.449994\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.748179 | 0.207508 | 0.103754 | − | 0.994603i | \(-0.466915\pi\) | ||||
0.103754 | + | 0.994603i | \(0.466915\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.53402 | − | 3.77242i | 1.58473 | − | 0.914946i | 0.590578 | − | 0.806980i | \(-0.298900\pi\) |
0.994155 | − | 0.107966i | \(-0.0344336\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.11872 | + | 3.53264i | 1.40373 | + | 0.810444i | 0.994773 | − | 0.102109i | \(-0.0325591\pi\) |
0.408957 | + | 0.912553i | \(0.365892\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.88904 | + | 3.55717i | −0.630440 | + | 0.776238i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.63394 | + | 2.83006i | −0.340699 | + | 0.590109i | −0.984563 | − | 0.175032i | \(-0.943997\pi\) |
0.643863 | + | 0.765141i | \(0.277331\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.95123 | − | 3.37458i | 0.760414 | − | 0.649439i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 2.48504i | − | 0.461460i | −0.973018 | − | 0.230730i | \(-0.925889\pi\) | ||
0.973018 | − | 0.230730i | \(-0.0741114\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.84372 | + | 3.95123i | −1.22917 | + | 0.709661i | −0.966856 | − | 0.255322i | \(-0.917819\pi\) |
−0.262313 | + | 0.964983i | \(0.584485\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.98646 | + | 2.83402i | −0.519876 | + | 0.493340i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.73959 | − | 2.15905i | −0.614784 | − | 0.354946i | 0.160051 | − | 0.987109i | \(-0.448834\pi\) |
−0.774835 | + | 0.632163i | \(0.782167\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.26008 | − | 0.302513i | 0.201774 | − | 0.0484409i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.8663 | 1.69703 | 0.848514 | − | 0.529173i | \(-0.177498\pi\) | ||||
0.848514 | + | 0.529173i | \(0.177498\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.03200i | 0.462375i | 0.972909 | + | 0.231188i | \(0.0742611\pi\) | ||||
−0.972909 | + | 0.231188i | \(0.925739\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.59088 | + | 3.22790i | 0.815514 | + | 0.470837i | 0.848867 | − | 0.528606i | \(-0.177285\pi\) |
−0.0333530 | + | 0.999444i | \(0.510619\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.83117 | − | 6.75624i | 0.261596 | − | 0.965178i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 9.47926 | − | 8.99541i | 1.32736 | − | 1.25961i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.0540095 | + | 0.0935472i | 0.00741878 | + | 0.0128497i | 0.869711 | − | 0.493561i | \(-0.164305\pi\) |
−0.862292 | + | 0.506411i | \(0.830972\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 11.7335 | + | 3.47567i | 1.55414 | + | 0.460363i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.60248 | + | 11.4358i | 0.859570 | + | 1.48882i | 0.872340 | + | 0.488900i | \(0.162602\pi\) |
−0.0127699 | + | 0.999918i | \(0.504065\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.90005 | + | 3.98375i | 0.883461 | + | 0.510067i | 0.871798 | − | 0.489865i | \(-0.162954\pi\) |
0.0116632 | + | 0.999932i | \(0.496287\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.42743 | + | 7.15910i | −0.431816 | + | 0.901962i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.09859 | − | 2.94367i | 0.622892 | − | 0.359627i | −0.155102 | − | 0.987898i | \(-0.549571\pi\) |
0.777994 | + | 0.628272i | \(0.216237\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.60758 | + | 5.42703i | −0.193530 | + | 0.653338i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.9589i | 1.65662i | 0.560273 | + | 0.828308i | \(0.310696\pi\) | ||||
−0.560273 | + | 0.828308i | \(0.689304\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.780701 | + | 1.35221i | 0.0913742 | + | 0.158265i | 0.908090 | − | 0.418776i | \(-0.137541\pi\) |
−0.816715 | + | 0.577041i | \(0.804207\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.41505 | − | 5.80681i | 0.275220 | − | 0.661747i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.27644 | − | 2.21086i | 0.143611 | − | 0.248742i | −0.785243 | − | 0.619188i | \(-0.787462\pi\) |
0.928854 | + | 0.370446i | \(0.120795\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.29018 | − | 7.28107i | 0.587798 | − | 0.809008i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.901948i | 0.0990016i | 0.998774 | + | 0.0495008i | \(0.0157630\pi\) | ||||
−0.998774 | + | 0.0495008i | \(0.984237\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.00478 | − | 4.18529i | −0.107724 | − | 0.448710i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.43223 | − | 4.21274i | 0.257816 | − | 0.446550i | −0.707841 | − | 0.706372i | \(-0.750331\pi\) |
0.965656 | + | 0.259822i | \(0.0836640\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.57217 | + | 1.20278i | −0.164808 | + | 0.126086i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −9.92856 | + | 9.42178i | −1.02954 | + | 0.976993i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −12.9183 | −1.31166 | −0.655829 | − | 0.754909i | \(-0.727681\pi\) | ||||
−0.655829 | + | 0.754909i | \(0.727681\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.88390 | + | 5.98057i | −0.390346 | + | 0.601070i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.56718 | + | 2.71443i | 0.155940 | + | 0.270096i | 0.933401 | − | 0.358835i | \(-0.116826\pi\) |
−0.777461 | + | 0.628931i | \(0.783493\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.89048 | − | 13.6667i | 0.777472 | − | 1.34662i | −0.155922 | − | 0.987769i | \(-0.549835\pi\) |
0.933394 | − | 0.358852i | \(-0.116832\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.92544 | − | 11.9952i | 0.669508 | − | 1.15962i | −0.308534 | − | 0.951213i | \(-0.599839\pi\) |
0.978042 | − | 0.208408i | \(-0.0668282\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.863166 | − | 1.49505i | −0.0826763 | − | 0.143200i | 0.821722 | − | 0.569888i | \(-0.193013\pi\) |
−0.904399 | + | 0.426688i | \(0.859680\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.17117 | − | 2.12423i | −0.680657 | − | 0.201623i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.93811 | −0.464539 | −0.232269 | − | 0.972652i | \(-0.574615\pi\) | ||||
−0.232269 | + | 0.972652i | \(0.574615\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.99991 | − | 1.01898i | 0.184891 | − | 0.0942050i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −7.66554 | + | 18.4313i | −0.702699 | + | 1.68959i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.67489 | + | 4.63305i | −0.243172 | + | 0.421186i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 18.3009 | − | 4.39359i | 1.65014 | − | 0.396157i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 15.9416i | − | 1.41458i | −0.706921 | − | 0.707292i | \(-0.749917\pi\) | ||
0.706921 | − | 0.707292i | \(-0.250083\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.22593 | + | 5.10648i | 0.107938 | + | 0.449600i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.17025 | + | 7.22309i | −0.364357 | + | 0.631084i | −0.988673 | − | 0.150087i | \(-0.952044\pi\) |
0.624316 | + | 0.781172i | \(0.285378\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −18.5366 | + | 2.41328i | −1.60732 | + | 0.209258i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.01096 | + | 6.94718i | 0.342679 | + | 0.593537i | 0.984929 | − | 0.172958i | \(-0.0553323\pi\) |
−0.642250 | + | 0.766495i | \(0.721999\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 4.61654i | − | 0.391570i | −0.980647 | − | 0.195785i | \(-0.937275\pi\) | ||
0.980647 | − | 0.195785i | \(-0.0627254\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 10.7213 | + | 3.17584i | 0.902895 | + | 0.267454i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.54017 | + | 0.889218i | −0.128796 | + | 0.0743601i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.352278 | − | 12.1192i | 0.0290554 | − | 0.999578i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 15.6215 | + | 9.01906i | 1.27976 | + | 0.738870i | 0.976804 | − | 0.214134i | \(-0.0686931\pi\) |
0.302956 | + | 0.953004i | \(0.402026\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.12850 | + | 3.68667i | 0.173215 | + | 0.300017i | 0.939542 | − | 0.342434i | \(-0.111251\pi\) |
−0.766327 | + | 0.642451i | \(0.777918\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 12.3278 | − | 18.9828i | 0.996643 | − | 1.53467i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.32830 | − | 14.4250i | −0.664671 | − | 1.15124i | −0.979374 | − | 0.202054i | \(-0.935238\pi\) |
0.314703 | − | 0.949190i | \(-0.398095\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.128787 | + | 0.135714i | 0.0102135 | + | 0.0107628i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.11620 | − | 8.57363i | −0.0879690 | − | 0.675697i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −13.9950 | − | 8.07999i | −1.09617 | − | 0.632874i | −0.160957 | − | 0.986961i | \(-0.551458\pi\) |
−0.935212 | + | 0.354087i | \(0.884792\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 17.4029i | − | 1.34668i | −0.739335 | − | 0.673338i | \(-0.764860\pi\) | ||
0.739335 | − | 0.673338i | \(-0.235140\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.4402 | −0.956941 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 21.1668 | + | 1.10948i | 1.61867 | + | 0.0848438i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −17.0267 | − | 9.83038i | −1.29452 | − | 0.747390i | −0.315066 | − | 0.949070i | \(-0.602027\pi\) |
−0.979451 | + | 0.201680i | \(0.935360\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 15.7437 | + | 16.5906i | 1.18337 | + | 1.24702i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.84722 | − | 3.37589i | 0.437042 | − | 0.252326i | −0.265300 | − | 0.964166i | \(-0.585471\pi\) |
0.702342 | + | 0.711840i | \(0.252138\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.71256i | 0.573270i | 0.958040 | + | 0.286635i | \(0.0925367\pi\) | ||||
−0.958040 | + | 0.286635i | \(0.907463\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 13.2318 | + | 3.91950i | 0.978123 | + | 0.289737i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −8.96711 | + | 15.5315i | −0.655740 | + | 1.13577i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.87781 | + | 13.4431i | −0.209330 | + | 0.977845i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −12.7009 | − | 7.33284i | −0.919001 | − | 0.530586i | −0.0356850 | − | 0.999363i | \(-0.511361\pi\) |
−0.883316 | + | 0.468777i | \(0.844695\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.21969 | + | 5.32299i | −0.663648 | + | 0.383157i | −0.793666 | − | 0.608354i | \(-0.791830\pi\) |
0.130018 | + | 0.991512i | \(0.458497\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 7.53462 | 0.536820 | 0.268410 | − | 0.963305i | \(-0.413502\pi\) | ||||
0.268410 | + | 0.963305i | \(0.413502\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.993782 | + | 0.573760i | −0.0704473 | + | 0.0406728i | −0.534810 | − | 0.844972i | \(-0.679617\pi\) |
0.464363 | + | 0.885645i | \(0.346283\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7.39680 | − | 7.01924i | 0.521730 | − | 0.495099i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.99497 | + | 5.22188i | 0.280392 | + | 0.366504i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.513161 | + | 9.79018i | −0.0356671 | + | 0.680465i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −16.7943 | −1.16169 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.1248 | −0.765862 | −0.382931 | − | 0.923777i | \(-0.625085\pi\) | ||||
−0.382931 | + | 0.923777i | \(0.625085\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 5.64404 | + | 23.5095i | 0.386723 | + | 1.61085i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.02888 | − | 19.3049i | 0.545036 | − | 1.31050i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.86160 | + | 1.96173i | 0.125795 | + | 0.132561i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.88862 | − | 2.82245i | 0.328844 | − | 0.189858i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −10.6904 | −0.715883 | −0.357942 | − | 0.933744i | \(-0.616521\pi\) | ||||
−0.357942 | + | 0.933744i | \(0.616521\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −11.5979 | + | 6.69603i | −0.769777 | + | 0.444431i | −0.832795 | − | 0.553581i | \(-0.813261\pi\) |
0.0630180 | + | 0.998012i | \(0.479927\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.32905 | − | 4.80878i | −0.550399 | − | 0.317773i | 0.198884 | − | 0.980023i | \(-0.436268\pi\) |
−0.749283 | + | 0.662250i | \(0.769602\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.71953 | − | 10.7563i | 0.113137 | − | 0.707712i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −10.7087 | + | 18.5481i | −0.701552 | + | 1.21512i | 0.266369 | + | 0.963871i | \(0.414176\pi\) |
−0.967921 | + | 0.251253i | \(0.919157\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.25586 | − | 4.23964i | 0.0815766 | − | 0.275394i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 25.2806i | − | 1.63527i | −0.575738 | − | 0.817634i | \(-0.695285\pi\) | ||
0.575738 | − | 0.817634i | \(-0.304715\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −19.7291 | + | 11.3906i | −1.27086 | + | 0.733733i | −0.975150 | − | 0.221543i | \(-0.928891\pi\) |
−0.295713 | + | 0.955277i | \(0.595557\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 5.96573 | − | 14.4017i | 0.382702 | − | 0.923872i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.57790 | + | 2.64305i | 0.291285 | + | 0.168173i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.364687 | + | 1.51906i | 0.0231111 | + | 0.0962663i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 16.4201 | 1.03643 | 0.518215 | − | 0.855251i | \(-0.326597\pi\) | ||||
0.518215 | + | 0.855251i | \(0.326597\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 7.76780i | − | 0.488357i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 10.2616 | + | 5.92452i | 0.640100 | + | 0.369562i | 0.784653 | − | 0.619935i | \(-0.212841\pi\) |
−0.144553 | + | 0.989497i | \(0.546175\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 11.3290 | − | 1.47493i | 0.703951 | − | 0.0916474i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.38450 | − | 6.64258i | −0.209495 | − | 0.411165i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.76844 | + | 4.79507i | 0.170709 | + | 0.295677i | 0.938668 | − | 0.344822i | \(-0.112061\pi\) |
−0.767959 | + | 0.640499i | \(0.778727\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.39300 | − | 8.07851i | 0.146449 | − | 0.494397i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −0.504112 | − | 0.873148i | −0.0307363 | − | 0.0532368i | 0.850248 | − | 0.526382i | \(-0.176452\pi\) |
−0.880984 | + | 0.473145i | \(0.843119\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.991979 | + | 0.572720i | 0.0602585 | + | 0.0347902i | 0.529827 | − | 0.848106i | \(-0.322257\pi\) |
−0.469568 | + | 0.882896i | \(0.655590\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.16152 | + | 2.66140i | −0.130821 | + | 0.161075i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8.08299 | + | 4.66672i | −0.485660 | + | 0.280396i | −0.722772 | − | 0.691086i | \(-0.757132\pi\) |
0.237112 | + | 0.971482i | \(0.423799\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −12.9121 | + | 19.8826i | −0.773028 | + | 1.19034i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.922818i | 0.0550507i | 0.999621 | + | 0.0275253i | \(0.00876270\pi\) | ||||
−0.999621 | + | 0.0275253i | \(0.991237\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.77681 | + | 6.54162i | 0.224508 | + | 0.388859i | 0.956172 | − | 0.292807i | \(-0.0945892\pi\) |
−0.731664 | + | 0.681666i | \(0.761256\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −22.8336 | + | 17.4688i | −1.34783 | + | 1.03115i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 19.9623 | − | 34.5757i | 1.17425 | − | 2.03386i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −21.7570 | + | 5.22330i | −1.27542 | + | 0.306195i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 21.3909i | − | 1.24967i | −0.780758 | − | 0.624834i | \(-0.785167\pi\) | ||
0.780758 | − | 0.624834i | \(-0.214833\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −4.12310 | + | 11.6428i | −0.239247 | + | 0.675586i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.22248 | + | 2.11739i | −0.0706977 | + | 0.122452i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.87427 | − | 6.37122i | −0.280949 | − | 0.367231i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.73696 | + | 3.93797i | 0.214683 | + | 0.226230i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −16.7500 | −0.955972 | −0.477986 | − | 0.878368i | \(-0.658633\pi\) | ||||
−0.477986 | + | 0.878368i | \(0.658633\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7.76322 | − | 26.2078i | 0.441634 | − | 1.49091i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.52577 | + | 4.37477i | 0.143224 | + | 0.248070i | 0.928709 | − | 0.370810i | \(-0.120920\pi\) |
−0.785485 | + | 0.618880i | \(0.787587\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.50546 | − | 12.9998i | 0.424234 | − | 0.734795i | −0.572115 | − | 0.820174i | \(-0.693877\pi\) |
0.996349 | + | 0.0853790i | \(0.0272101\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −12.7324 | + | 22.0531i | −0.715121 | + | 1.23863i | 0.247792 | + | 0.968813i | \(0.420295\pi\) |
−0.962913 | + | 0.269812i | \(0.913038\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.95349 | + | 5.11559i | 0.165364 | + | 0.286418i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6.81374 | − | 23.0025i | 0.380306 | − | 1.28387i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 53.3065 | 2.96605 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2.05824 | − | 2.16895i | −0.113821 | − | 0.119943i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −16.9375 | + | 2.20509i | −0.933794 | + | 0.121571i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.45134 | + | 9.44199i | −0.299633 | + | 0.518979i | −0.976052 | − | 0.217538i | \(-0.930197\pi\) |
0.676419 | + | 0.736517i | \(0.263531\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −12.9365 | − | 0.678080i | −0.708918 | − | 0.0371585i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 18.4210i | 1.00345i | 0.865026 | + | 0.501727i | \(0.167302\pi\) | ||||
−0.865026 | + | 0.501727i | \(0.832698\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −8.31675 | + | 1.99664i | −0.451704 | + | 0.108443i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 9.39213 | − | 16.2677i | 0.508613 | − | 0.880943i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 7.01353 | + | 17.1409i | 0.378695 | + | 0.925522i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4.79206 | − | 8.30010i | −0.257252 | − | 0.445573i | 0.708253 | − | 0.705959i | \(-0.249484\pi\) |
−0.965505 | + | 0.260386i | \(0.916150\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 16.5601i | 0.886441i | 0.896413 | + | 0.443220i | \(0.146164\pi\) | ||||
−0.896413 | + | 0.443220i | \(0.853836\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.95623 | − | 2.52479i | 0.157792 | − | 0.134764i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 15.5984 | − | 9.00574i | 0.830219 | − | 0.479327i | −0.0237089 | − | 0.999719i | \(-0.507547\pi\) |
0.853928 | + | 0.520392i | \(0.174214\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −5.45792 | + | 34.1413i | −0.288864 | + | 1.80695i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.47735 | − | 2.00765i | −0.183527 | − | 0.105960i | 0.405422 | − | 0.914130i | \(-0.367125\pi\) |
−0.588949 | + | 0.808170i | \(0.700458\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.4592 | + | 26.7760i | 0.813640 | + | 1.40927i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.63175 | + | 8.88451i | −0.138131 | + | 0.466316i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 17.0259 | + | 29.4897i | 0.888744 | + | 1.53935i | 0.841361 | + | 0.540473i | \(0.181755\pi\) |
0.0473832 | + | 0.998877i | \(0.484912\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 29.0459 | − | 14.7993i | 1.51207 | − | 0.770423i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.263879 | − | 0.109747i | −0.0136999 | − | 0.00569779i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −11.6169 | − | 6.70705i | −0.601503 | − | 0.347278i | 0.168130 | − | 0.985765i | \(-0.446227\pi\) |
−0.769632 | + | 0.638487i | \(0.779561\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 1.85925i | − | 0.0957564i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 15.3945 | 0.790764 | 0.395382 | − | 0.918517i | \(-0.370612\pi\) | ||||
0.395382 | + | 0.918517i | \(0.370612\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6.44569 | − | 26.8487i | −0.330223 | − | 1.37550i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 21.1422 | + | 12.2065i | 1.08032 | + | 0.623722i | 0.930982 | − | 0.365065i | \(-0.118953\pi\) |
0.149336 | + | 0.988787i | \(0.452287\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.12943 | + | 8.10462i | 0.209911 | + | 0.411981i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 30.1938 | − | 17.4324i | 1.53089 | − | 0.883857i | 0.531564 | − | 0.847018i | \(-0.321604\pi\) |
0.999321 | − | 0.0368391i | \(-0.0117289\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 24.6556i | 1.24689i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4.10299 | + | 13.8513i | −0.206969 | + | 0.698704i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 11.2631 | − | 19.5083i | 0.565281 | − | 0.979095i | −0.431743 | − | 0.901997i | \(-0.642101\pi\) |
0.997024 | − | 0.0770980i | \(-0.0245654\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −30.2434 | + | 11.5594i | −1.51407 | + | 0.578692i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −15.8774 | − | 9.16683i | −0.792881 | − | 0.457770i | 0.0480950 | − | 0.998843i | \(-0.484685\pi\) |
−0.840976 | + | 0.541073i | \(0.818018\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.12033 | + | 2.95623i | −0.255062 | + | 0.147260i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 10.2642 | 0.508778 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9.37130 | + | 5.41052i | −0.463381 | + | 0.267533i | −0.713465 | − | 0.700691i | \(-0.752875\pi\) |
0.250084 | + | 0.968224i | \(0.419542\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 9.56420 | + | 10.0786i | 0.471767 | + | 0.497143i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −32.2584 | − | 13.4162i | −1.58733 | − | 0.660169i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.86662 | − | 7.77516i | −0.0914086 | − | 0.380751i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −34.1164 | −1.66670 | −0.833348 | − | 0.552749i | \(-0.813579\pi\) | ||||
−0.833348 | + | 0.552749i | \(0.813579\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −29.9892 | −1.46158 | −0.730792 | − | 0.682600i | \(-0.760849\pi\) | ||||
−0.730792 | + | 0.682600i | \(0.760849\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 19.3408 | + | 1.01377i | 0.940384 | + | 0.0492910i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −20.9036 | + | 2.72144i | −1.01160 | + | 0.131700i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.23441 | + | 2.12036i | −0.107878 | + | 0.102372i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −32.6954 | + | 18.8767i | −1.57488 | + | 0.909258i | −0.579324 | + | 0.815097i | \(0.696684\pi\) |
−0.995557 | + | 0.0941612i | \(0.969983\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0.221375 | 0.0106386 | 0.00531930 | − | 0.999986i | \(-0.498307\pi\) | ||||
0.00531930 | + | 0.999986i | \(0.498307\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −19.9952 | + | 11.5442i | −0.956501 | + | 0.552236i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12.5292 | + | 7.23374i | 0.597987 | + | 0.345248i | 0.768249 | − | 0.640151i | \(-0.221128\pi\) |
−0.170262 | + | 0.985399i | \(0.554462\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4.30690 | − | 20.5536i | −0.205090 | − | 0.978743i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5.55285 | + | 9.61783i | −0.263824 | + | 0.456957i | −0.967255 | − | 0.253807i | \(-0.918317\pi\) |
0.703431 | + | 0.710764i | \(0.251651\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 29.9563 | + | 8.87359i | 1.41688 | + | 0.419707i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 31.1416i | − | 1.46966i | −0.678250 | − | 0.734831i | \(-0.737261\pi\) | ||
0.678250 | − | 0.734831i | \(-0.262739\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −22.3689 | + | 12.9147i | −1.05331 | + | 0.608128i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5.07545 | + | 5.34845i | 0.238466 | + | 0.251292i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −16.4171 | − | 9.47844i | −0.767962 | − | 0.443383i | 0.0641853 | − | 0.997938i | \(-0.479555\pi\) |
−0.832147 | + | 0.554555i | \(0.812888\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 13.0871 | − | 36.9553i | 0.610851 | − | 1.72492i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −15.1960 | −0.707746 | −0.353873 | − | 0.935293i | \(-0.615136\pi\) | ||||
−0.353873 | + | 0.935293i | \(0.615136\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 29.3400i | − | 1.36355i | −0.731564 | − | 0.681773i | \(-0.761209\pi\) | ||
0.731564 | − | 0.681773i | \(-0.238791\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −14.5382 | − | 8.39365i | −0.672749 | − | 0.388412i | 0.124369 | − | 0.992236i | \(-0.460309\pi\) |
−0.797117 | + | 0.603824i | \(0.793643\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.98153 | + | 14.3822i | −0.276201 | + | 0.664107i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −19.8590 | − | 20.9272i | −0.915055 | − | 0.964274i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.60356 | − | 6.24154i | −0.165692 | − | 0.286986i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.271776 | + | 0.176496i | 0.0124438 | + | 0.00808121i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.07579 | − | 1.86333i | −0.0491542 | − | 0.0851376i | 0.840401 | − | 0.541964i | \(-0.182319\pi\) |
−0.889556 | + | 0.456827i | \(0.848986\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.79788 | − | 1.61536i | −0.127572 | − | 0.0736540i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −5.34650 | − | 13.9884i | −0.243274 | − | 0.636492i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.02174 | − | 1.74460i | 0.136928 | − | 0.0790555i | −0.429971 | − | 0.902843i | \(-0.641476\pi\) |
0.566899 | + | 0.823787i | \(0.308143\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −26.8373 | − | 7.94967i | −1.21362 | − | 0.359497i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 26.1361i | − | 1.17950i | −0.807584 | − | 0.589752i | \(-0.799225\pi\) | ||
0.807584 | − | 0.589752i | \(-0.200775\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −9.37460 | − | 16.2373i | −0.422211 | − | 0.731290i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −22.4405 | − | 29.3322i | −1.00659 | − | 1.31573i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.15545 | − | 12.3936i | 0.320322 | − | 0.554814i | −0.660232 | − | 0.751061i | \(-0.729542\pi\) |
0.980554 | + | 0.196247i | \(0.0628756\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −7.03656 | − | 29.3099i | −0.314370 | − | 1.30947i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 39.3226i | − | 1.75331i | −0.481123 | − | 0.876653i | \(-0.659771\pi\) | ||
0.481123 | − | 0.876653i | \(-0.340229\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −20.9518 | + | 5.02999i | −0.930501 | + | 0.223390i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 17.4284 | − | 30.1868i | 0.772498 | − | 1.33801i | −0.163692 | − | 0.986512i | \(-0.552340\pi\) |
0.936190 | − | 0.351495i | \(-0.114326\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.81435 | − | 1.58638i | −0.168737 | − | 0.0701774i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 36.0977 | − | 6.68985i | 1.59375 | − | 0.295364i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −15.3455 | −0.674896 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −32.6511 | − | 9.67183i | −1.43322 | − | 0.424546i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −12.3030 | − | 21.3094i | −0.539005 | − | 0.933584i | −0.998958 | − | 0.0456406i | \(-0.985467\pi\) |
0.459953 | − | 0.887943i | \(-0.347866\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −13.8335 | + | 23.9603i | −0.604897 | + | 1.04771i | 0.387171 | + | 0.922008i | \(0.373452\pi\) |
−0.992068 | + | 0.125704i | \(0.959881\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −29.8114 | + | 51.6348i | −1.29860 | + | 2.24925i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.16050 | + | 10.6703i | 0.267848 | + | 0.463926i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 33.2237 | + | 21.5761i | 1.44178 | + | 0.936322i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8.12993 | 0.352146 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 8.48288 | − | 8.04989i | 0.366063 | − | 0.347378i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4.26029 | + | 16.0845i | 0.183504 | + | 0.692808i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.90334 | − | 13.6890i | 0.339791 | − | 0.588536i | −0.644602 | − | 0.764518i | \(-0.722977\pi\) |
0.984393 | + | 0.175983i | \(0.0563103\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.11844 | + | 12.9895i | 0.133825 | + | 0.557431i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 13.9288i | − | 0.595553i | −0.954636 | − | 0.297776i | \(-0.903755\pi\) | ||
0.954636 | − | 0.297776i | \(-0.0962450\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 23.8697 | + | 1.25115i | 1.01873 | + | 0.0533978i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 8.77875 | − | 15.2052i | 0.373987 | − | 0.647765i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.871984 | + | 6.69778i | 0.0370805 | + | 0.284818i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 17.2950 | + | 29.9559i | 0.732814 | + | 1.26927i | 0.955676 | + | 0.294421i | \(0.0951269\pi\) |
−0.222862 | + | 0.974850i | \(0.571540\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.26848i | 0.0959464i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8.82248 | + | 29.7838i | −0.372485 | + | 1.25747i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −25.0789 | + | 14.4793i | −1.05695 | + | 0.610229i | −0.924586 | − | 0.380972i | \(-0.875589\pi\) |
−0.132361 | + | 0.991202i | \(0.542256\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.588712 | + | 23.8045i | 0.0247236 | + | 0.999694i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 10.1544 | + | 5.86266i | 0.425696 | + | 0.245775i | 0.697511 | − | 0.716574i | \(-0.254291\pi\) |
−0.271816 | + | 0.962349i | \(0.587624\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 17.5541 | + | 30.4045i | 0.734614 | + | 1.27239i | 0.954892 | + | 0.296952i | \(0.0959703\pi\) |
−0.220278 | + | 0.975437i | \(0.570696\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −24.3556 | − | 7.21457i | −1.01747 | − | 0.301393i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10.0423 | + | 17.3937i | 0.418065 | + | 0.724110i | 0.995745 | − | 0.0921536i | \(-0.0293751\pi\) |
−0.577680 | + | 0.816263i | \(0.696042\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −13.3755 | + | 12.6928i | −0.555867 | + | 0.527494i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.44998 | − | 1.89529i | −0.0601554 | − | 0.0786298i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.222363 | − | 0.128382i | −0.00920935 | − | 0.00531702i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 32.7111i | − | 1.35013i | −0.737757 | − | 0.675066i | \(-0.764115\pi\) | ||
0.737757 | − | 0.675066i | \(-0.235885\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −55.8331 | −2.30056 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 12.6898 | − | 3.04649i | 0.521988 | − | 0.125316i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 3.86664 | + | 2.23240i | 0.158784 | + | 0.0916738i | 0.577286 | − | 0.816542i | \(-0.304112\pi\) |
−0.418503 | + | 0.908216i | \(0.637445\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.44173 | + | 1.36814i | −0.0590062 | + | 0.0559944i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −31.6126 | + | 18.2515i | −1.29165 | + | 0.745737i | −0.978947 | − | 0.204112i | \(-0.934569\pi\) |
−0.312707 | + | 0.949850i | \(0.601236\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 32.4566i | − | 1.32393i | −0.749534 | − | 0.661966i | \(-0.769722\pi\) | ||
0.749534 | − | 0.661966i | \(-0.230278\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 9.61955 | − | 14.8125i | 0.391738 | − | 0.603213i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −10.4608 | + | 18.1187i | −0.424593 | + | 0.735416i | −0.996382 | − | 0.0849841i | \(-0.972916\pi\) |
0.571790 | + | 0.820400i | \(0.306249\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 8.83970 | + | 7.17937i | 0.358203 | + | 0.290923i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.18298 | + | 2.41505i | 0.169225 | + | 0.0977023i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 33.6783 | − | 19.4442i | 1.36025 | − | 0.785343i | 0.370596 | − | 0.928794i | \(-0.379153\pi\) |
0.989657 | + | 0.143451i | \(0.0458200\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 12.8874 | 0.518828 | 0.259414 | − | 0.965766i | \(-0.416471\pi\) | ||||
0.259414 | + | 0.965766i | \(0.416471\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8.89767 | + | 5.13707i | −0.357628 | + | 0.206476i | −0.668040 | − | 0.744126i | \(-0.732866\pi\) |
0.310412 | + | 0.950602i | \(0.399533\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.09423 | + | 16.6961i | 0.124167 | + | 0.669990i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.66154 | + | 12.7624i | 0.0665683 | + | 0.511316i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −28.2849 | + | 6.79049i | −1.12959 | + | 0.271186i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −32.5794 | −1.29902 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 44.9308 | 1.78866 | 0.894332 | − | 0.447403i | \(-0.147651\pi\) | ||||
0.894332 | + | 0.447403i | \(0.147651\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −18.7363 | + | 4.49811i | −0.744701 | + | 0.178784i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.37004 | − | 5.05488i | 0.0542831 | − | 0.200282i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 19.0113 | + | 37.3126i | 0.752076 | + | 1.47606i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 33.7953 | − | 19.5118i | 1.33484 | − | 0.770668i | 0.348799 | − | 0.937197i | \(-0.386589\pi\) |
0.986036 | + | 0.166529i | \(0.0532561\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 12.2206 | 0.481932 | 0.240966 | − | 0.970534i | \(-0.422536\pi\) | ||||
0.240966 | + | 0.970534i | \(0.422536\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −14.6082 | + | 8.43406i | −0.574308 | + | 0.331577i | −0.758868 | − | 0.651244i | \(-0.774247\pi\) |
0.184560 | + | 0.982821i | \(0.440914\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −27.1832 | − | 15.6942i | −1.06703 | − | 0.616052i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5.71662 | − | 35.7595i | 0.224052 | − | 1.40153i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −10.8531 | + | 18.7980i | −0.424713 | + | 0.735624i | −0.996394 | − | 0.0848520i | \(-0.972958\pi\) |
0.571681 | + | 0.820476i | \(0.306292\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3.92849 | + | 2.55123i | 0.153265 | + | 0.0995331i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 36.3752i | − | 1.41698i | −0.705722 | − | 0.708489i | \(-0.749377\pi\) | ||
0.705722 | − | 0.708489i | \(-0.250623\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12.9940 | − | 7.50207i | 0.505407 | − | 0.291797i | −0.225537 | − | 0.974235i | \(-0.572414\pi\) |
0.730944 | + | 0.682438i | \(0.239080\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 7.09219 | − | 6.73018i | 0.275438 | − | 0.261379i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.03281 | + | 4.06039i | 0.272311 | + | 0.157219i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −18.0048 | + | 4.32248i | −0.696104 | + | 0.167117i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −18.9389 | −0.731127 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 0.119232i | − | 0.00459606i | −0.999997 | − | 0.00229803i | \(-0.999269\pi\) | ||
0.999997 | − | 0.00229803i | \(-0.000731486\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −20.6622 | − | 11.9293i | −0.794114 | − | 0.458482i | 0.0472948 | − | 0.998881i | \(-0.484940\pi\) |
−0.841409 | + | 0.540399i | \(0.818273\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 27.1457 | − | 20.7677i | 1.04176 | − | 0.796990i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −16.8256 | + | 15.9668i | −0.644760 | + | 0.611850i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 14.6082 | + | 25.3022i | 0.558968 | + | 0.968161i | 0.997583 | + | 0.0694856i | \(0.0221358\pi\) |
−0.438615 | + | 0.898675i | \(0.644531\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −15.9721 | − | 4.73122i | −0.609374 | − | 0.180507i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.0404088 | + | 0.0699901i | 0.00153945 | + | 0.00266641i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −36.0356 | − | 20.8052i | −1.37086 | − | 0.791465i | −0.379822 | − | 0.925059i | \(-0.624015\pi\) |
−0.991036 | + | 0.133594i | \(0.957348\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.45309 | − | 18.8110i | −0.0551984 | − | 0.714569i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 71.0005 | − | 40.9922i | 2.68934 | − | 1.55269i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −10.5360 | + | 35.5685i | −0.398509 | + | 1.34532i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 14.6976i | 0.555122i | 0.960708 | + | 0.277561i | \(0.0895261\pi\) | ||||
−0.960708 | + | 0.277561i | \(0.910474\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −15.2543 | − | 26.4213i | −0.575328 | − | 0.996497i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −7.65690 | − | 3.18450i | −0.287967 | − | 0.119765i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −18.6403 | + | 32.2859i | −0.700050 | + | 1.21252i | 0.268398 | + | 0.963308i | \(0.413506\pi\) |
−0.968448 | + | 0.249214i | \(0.919828\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.400885 | − | 7.64816i | 0.0150343 | − | 0.286828i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 25.8242i | − | 0.967125i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −10.2218 | − | 42.5776i | −0.381740 | − | 1.59009i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −15.8612 | + | 27.4724i | −0.591522 | + | 1.02455i | 0.402505 | + | 0.915418i | \(0.368139\pi\) |
−0.994028 | + | 0.109129i | \(0.965194\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.39027 | + | 41.4031i | 0.200744 | + | 1.54193i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −28.6221 | + | 27.1611i | −1.06447 | + | 1.01013i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −30.3126 | −1.12423 | −0.562117 | − | 0.827058i | \(-0.690013\pi\) | ||||
−0.562117 | + | 0.827058i | \(0.690013\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 4.22437 | − | 26.6675i | 0.156458 | − | 0.987685i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 11.4380 | + | 19.8111i | 0.423048 | + | 0.732741i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.19316 | − | 2.06661i | 0.0440703 | − | 0.0763321i | −0.843149 | − | 0.537680i | \(-0.819301\pi\) |
0.887219 | + | 0.461348i | \(0.152634\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −6.99716 | + | 12.1194i | −0.257744 | + | 0.446425i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.29721 | − | 3.97889i | −0.0845043 | − | 0.146366i | 0.820676 | − | 0.571394i | \(-0.193597\pi\) |
−0.905180 | + | 0.425029i | \(0.860264\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 8.77875 | + | 2.60042i | 0.322496 | + | 0.0955289i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 12.5047 | 0.458753 | 0.229376 | − | 0.973338i | \(-0.426331\pi\) | ||||
0.229376 | + | 0.973338i | \(0.426331\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.22841 | + | 2.41093i | 0.0449451 | + | 0.0882114i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.73102 | + | 36.3393i | 0.172868 | + | 1.32781i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −17.3708 | + | 30.0872i | −0.633871 | + | 1.09790i | 0.352883 | + | 0.935668i | \(0.385202\pi\) |
−0.986753 | + | 0.162229i | \(0.948132\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 27.6547 | − | 6.63919i | 1.00779 | − | 0.241946i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 14.5066i | − | 0.527250i | −0.964625 | − | 0.263625i | \(-0.915082\pi\) | ||
0.964625 | − | 0.263625i | \(-0.0849182\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3.14077 | − | 13.0825i | −0.114003 | − | 0.474864i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −20.2457 | + | 35.0666i | −0.733906 | + | 1.27116i | 0.221296 | + | 0.975207i | \(0.428971\pi\) |
−0.955202 | + | 0.295955i | \(0.904362\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.21725 | + | 1.75395i | 0.152675 | + | 0.0634973i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.93984 | + | 8.55606i | 0.178367 | + | 0.308941i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 39.6907i | − | 1.43128i | −0.698468 | − | 0.715641i | \(-0.746135\pi\) | ||
0.698468 | − | 0.715641i | \(-0.253865\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 19.6780 | + | 5.82897i | 0.708685 | + | 0.209925i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −4.90181 | + | 2.83006i | −0.176306 | + | 0.101790i | −0.585556 | − | 0.810632i | \(-0.699124\pi\) |
0.409250 | + | 0.912422i | \(0.365790\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 18.4839 | − | 7.06475i | 0.663107 | − | 0.253447i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 66.4877 | + | 38.3867i | 2.38217 | + | 1.37535i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −16.5903 | − | 28.7352i | −0.593647 | − | 1.02823i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −8.38596 | − | 9.81894i | −0.299690 | − | 0.350900i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.59485 | + | 2.76237i | 0.0568504 | + | 0.0984677i | 0.893050 | − | 0.449958i | \(-0.148561\pi\) |
−0.836200 | + | 0.548425i | \(0.815228\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 6.60139 | + | 6.95647i | 0.235016 | + | 0.247657i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 10.3766 | − | 7.93857i | 0.368949 | − | 0.282263i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.16248 | + | 2.98056i | 0.183325 | + | 0.105843i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 18.7853i | − | 0.665410i | −0.943031 | − | 0.332705i | \(-0.892039\pi\) | ||
0.943031 | − | 0.332705i | \(-0.107961\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 48.7079 | 1.72316 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.763875 | − | 14.5734i | 0.0269902 | − | 0.514924i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −3.21424 | − | 1.85574i | −0.113428 | − | 0.0654877i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.20207 | − | 1.26672i | −0.0423147 | − | 0.0445908i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 24.5995 | − | 14.2025i | 0.864873 | − | 0.499335i | −0.000767968 | − | 1.00000i | \(-0.500244\pi\) |
0.865641 | + | 0.500665i | \(0.166911\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 46.9628i | − | 1.64909i | −0.565799 | − | 0.824543i | \(-0.691432\pi\) | ||
0.565799 | − | 0.824543i | \(-0.308568\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.90226 | + | 0.563482i | 0.0667151 | + | 0.0197622i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −10.7110 | + | 18.5519i | −0.374729 | + | 0.649050i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.56433 | + | 5.35629i | −0.0896050 | + | 0.187164i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 16.9019 | + | 9.75831i | 0.589880 | + | 0.340567i | 0.765050 | − | 0.643971i | \(-0.222714\pi\) |
−0.175170 | + | 0.984538i | \(0.556048\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −21.7033 | + | 12.5304i | −0.756529 | + | 0.436782i | −0.828048 | − | 0.560657i | \(-0.810549\pi\) |
0.0715193 | + | 0.997439i | \(0.477215\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 40.2141 | 1.39838 | 0.699191 | − | 0.714935i | \(-0.253544\pi\) | ||||
0.699191 | + | 0.714935i | \(0.253544\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −5.52711 | + | 3.19108i | −0.191964 | + | 0.110831i | −0.592902 | − | 0.805275i | \(-0.702018\pi\) |
0.400937 | + | 0.916105i | \(0.368684\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −11.7264 | + | 11.1279i | −0.406785 | + | 0.386022i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −13.5225 | − | 51.0534i | −0.468526 | − | 1.76889i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −13.7074 | + | 38.7069i | −0.473796 | + | 1.33791i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −15.2513 | −0.526534 | −0.263267 | − | 0.964723i | \(-0.584800\pi\) | ||||
−0.263267 | + | 0.964723i | \(0.584800\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 22.8246 | 0.787055 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0.373125 | + | 1.55421i | 0.0128511 | + | 0.0535297i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.82732 | − | 14.0358i | −0.0627873 | − | 0.482274i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 9.00587 | + | 9.49028i | 0.309081 | + | 0.325706i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 12.2205 | − | 7.05551i | 0.418913 | − | 0.241860i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −16.7815 | −0.574586 | −0.287293 | − | 0.957843i | \(-0.592755\pi\) | ||||
−0.287293 | + | 0.957843i | \(0.592755\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 16.7758 | − | 9.68551i | 0.573050 | − | 0.330851i | −0.185317 | − | 0.982679i | \(-0.559331\pi\) |
0.758367 | + | 0.651828i | \(0.225998\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −42.4714 | − | 24.5208i | −1.44910 | − | 0.836641i | −0.450676 | − | 0.892688i | \(-0.648817\pi\) |
−0.998428 | + | 0.0560471i | \(0.982150\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −31.3931 | + | 38.6532i | −1.06987 | + | 1.31730i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 11.2358 | − | 19.4609i | 0.382470 | − | 0.662458i | −0.608944 | − | 0.793213i | \(-0.708407\pi\) |
0.991415 | + | 0.130755i | \(0.0417401\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 19.6403 | − | 66.3036i | 0.667020 | − | 2.25179i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6.06826i | 0.205851i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.81466 | − | 2.20239i | 0.129255 | − | 0.0746253i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −34.5311 | + | 17.5941i | −1.16870 | + | 0.595471i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 26.8618 | + | 15.5087i | 0.907059 | + | 0.523691i | 0.879484 | − | 0.475929i | \(-0.157888\pi\) |
0.0275755 | + | 0.999620i | \(0.491221\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −8.64902 | − | 36.0264i | −0.291724 | − | 1.21514i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 21.8713 | 0.736864 | 0.368432 | − | 0.929655i | \(-0.379895\pi\) | ||||
0.368432 | + | 0.929655i | \(0.379895\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 34.3430i | 1.15573i | 0.816131 | + | 0.577867i | \(0.196115\pi\) | ||||
−0.816131 | + | 0.577867i | \(0.803885\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 48.4807 | + | 27.9903i | 1.62782 | + | 0.939824i | 0.984741 | + | 0.174027i | \(0.0556779\pi\) |
0.643082 | + | 0.765797i | \(0.277655\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 25.6278 | + | 33.4985i | 0.859530 | + | 1.12350i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.23654 | + | 21.2759i | −0.0749268 | + | 0.712771i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 22.8060 | + | 39.5012i | 0.763175 | + | 1.32186i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.20276 | + | 4.06039i | −0.0401590 | + | 0.135573i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 9.81894 | + | 17.0069i | 0.327480 | + | 0.567212i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.705799 | + | 0.407493i | 0.0235136 | + | 0.0135756i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −10.7853 | − | 8.75956i | −0.358913 | − | 0.291500i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0.856413 | − | 0.494450i | 0.0284367 | − | 0.0164180i | −0.485714 | − | 0.874118i | \(-0.661440\pi\) |
0.514151 | + | 0.857700i | \(0.328107\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 7.88602 | + | 5.12133i | 0.261563 | + | 0.169864i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 28.5096i | 0.944567i | 0.881447 | + | 0.472283i | \(0.156570\pi\) | ||||
−0.881447 | + | 0.472283i | \(0.843430\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.07197 | − | 1.85671i | −0.0354771 | − | 0.0614482i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.84885 | − | 21.8822i | −0.0940774 | − | 0.722615i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.40350 | + | 2.43093i | −0.0462971 | + | 0.0801889i | −0.888245 | − | 0.459369i | \(-0.848075\pi\) |
0.841948 | + | 0.539558i | \(0.181409\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −28.2102 | + | 6.77256i | −0.929559 | + | 0.223163i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 10.4438i | 0.343761i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2.47812 | − | 47.2780i | 0.0813920 | − | 1.55281i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 6.57702 | − | 11.3917i | 0.215785 | − | 0.373751i | −0.737730 | − | 0.675096i | \(-0.764102\pi\) |
0.953515 | + | 0.301345i | \(0.0974356\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 35.0718 | − | 34.8707i | 1.14943 | − | 1.14284i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 6.02276 | + | 6.34672i | 0.197176 | + | 0.207782i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −20.2219 | −0.660622 | −0.330311 | − | 0.943872i | \(-0.607154\pi\) | ||||
−0.330311 | + | 0.943872i | \(0.607154\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 7.38441 | − | 24.9290i | 0.240981 | − | 0.813527i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −22.8119 | − | 39.5113i | −0.743646 | − | 1.28803i | −0.950825 | − | 0.309729i | \(-0.899762\pi\) |
0.207179 | − | 0.978303i | \(-0.433572\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −17.7548 | + | 30.7523i | −0.578177 | + | 1.00143i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 29.2959 | − | 50.7421i | 0.951990 | − | 1.64890i | 0.210880 | − | 0.977512i | \(-0.432367\pi\) |
0.741110 | − | 0.671383i | \(-0.234300\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.584105 | + | 1.01170i | 0.0189608 | + | 0.0328411i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −12.5270 | + | 42.2898i | −0.406216 | + | 1.37134i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −26.9224 | −0.872101 | −0.436051 | − | 0.899922i | \(-0.643623\pi\) | ||||
−0.436051 | + | 0.899922i | \(0.643623\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 7.04265 | + | 7.42147i | 0.227657 | + | 0.239902i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −19.5967 | − | 8.15025i | −0.632811 | − | 0.263185i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.7244 | − | 27.2354i | 0.507238 | − | 0.878562i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2.17503 | − | 41.4957i | 0.0700894 | − | 1.33718i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 17.4008i | 0.559572i | 0.960062 | + | 0.279786i | \(0.0902635\pi\) | ||||
−0.960062 | + | 0.279786i | \(0.909737\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 89.7785 | − | 21.5535i | 2.88410 | − | 0.692399i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −12.6200 | + | 21.8585i | −0.404996 | + | 0.701474i | −0.994321 | − | 0.106422i | \(-0.966060\pi\) |
0.589325 | + | 0.807896i | \(0.299394\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 7.42160 | + | 9.70087i | 0.237926 | + | 0.310996i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −3.74960 | − | 6.49450i | −0.119960 | − | 0.207778i | 0.799791 | − | 0.600278i | \(-0.204943\pi\) |
−0.919752 | + | 0.392501i | \(0.871610\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 11.5629i | 0.369552i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.34345 | − | 2.82072i | −0.138676 | − | 0.0900586i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −22.3498 | + | 12.9037i | −0.712848 | + | 0.411563i | −0.812115 | − | 0.583498i | \(-0.801684\pi\) |
0.0992666 | + | 0.995061i | \(0.468350\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −27.6345 | + | 10.5622i | −0.879615 | + | 0.336198i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −8.58074 | − | 4.95409i | −0.272852 | − | 0.157531i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −11.4009 | − | 19.7469i | −0.362161 | − | 0.627280i | 0.626156 | − | 0.779698i | \(-0.284627\pi\) |
−0.988316 | + | 0.152418i | \(0.951294\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −5.36341 | + | 18.1063i | −0.170203 | + | 0.574586i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.91662 | + | 10.2479i | 0.187381 | + | 0.324554i | 0.944376 | − | 0.328867i | \(-0.106667\pi\) |
−0.756995 | + | 0.653421i | \(0.773333\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −22.0618 | + | 4.08865i | −0.698006 | + | 0.129359i |
(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 | 2100.2.bo.i.1349.16 | 32 | ||
3.2 | odd | 2 | inner | 2100.2.bo.i.1349.6 | 32 | ||
5.2 | odd | 4 | 2100.2.bi.m.1601.4 | yes | 16 | ||
5.3 | odd | 4 | 2100.2.bi.l.1601.5 | yes | 16 | ||
5.4 | even | 2 | inner | 2100.2.bo.i.1349.1 | 32 | ||
7.3 | odd | 6 | inner | 2100.2.bo.i.1949.11 | 32 | ||
15.2 | even | 4 | 2100.2.bi.m.1601.7 | yes | 16 | ||
15.8 | even | 4 | 2100.2.bi.l.1601.2 | yes | 16 | ||
15.14 | odd | 2 | inner | 2100.2.bo.i.1349.11 | 32 | ||
21.17 | even | 6 | inner | 2100.2.bo.i.1949.1 | 32 | ||
35.3 | even | 12 | 2100.2.bi.l.101.2 | ✓ | 16 | ||
35.17 | even | 12 | 2100.2.bi.m.101.7 | yes | 16 | ||
35.24 | odd | 6 | inner | 2100.2.bo.i.1949.6 | 32 | ||
105.17 | odd | 12 | 2100.2.bi.m.101.4 | yes | 16 | ||
105.38 | odd | 12 | 2100.2.bi.l.101.5 | yes | 16 | ||
105.59 | even | 6 | inner | 2100.2.bo.i.1949.16 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2100.2.bi.l.101.2 | ✓ | 16 | 35.3 | even | 12 | ||
2100.2.bi.l.101.5 | yes | 16 | 105.38 | odd | 12 | ||
2100.2.bi.l.1601.2 | yes | 16 | 15.8 | even | 4 | ||
2100.2.bi.l.1601.5 | yes | 16 | 5.3 | odd | 4 | ||
2100.2.bi.m.101.4 | yes | 16 | 105.17 | odd | 12 | ||
2100.2.bi.m.101.7 | yes | 16 | 35.17 | even | 12 | ||
2100.2.bi.m.1601.4 | yes | 16 | 5.2 | odd | 4 | ||
2100.2.bi.m.1601.7 | yes | 16 | 15.2 | even | 4 | ||
2100.2.bo.i.1349.1 | 32 | 5.4 | even | 2 | inner | ||
2100.2.bo.i.1349.6 | 32 | 3.2 | odd | 2 | inner | ||
2100.2.bo.i.1349.11 | 32 | 15.14 | odd | 2 | inner | ||
2100.2.bo.i.1349.16 | 32 | 1.1 | even | 1 | trivial | ||
2100.2.bo.i.1949.1 | 32 | 21.17 | even | 6 | inner | ||
2100.2.bo.i.1949.6 | 32 | 35.24 | odd | 6 | inner | ||
2100.2.bo.i.1949.11 | 32 | 7.3 | odd | 6 | inner | ||
2100.2.bo.i.1949.16 | 32 | 105.59 | even | 6 | inner |