Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2100,2,Mod(101,2100)]
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, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2100.101");
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.bi (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(16.7685844245\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 3 x^{15} + 9 x^{14} - 18 x^{13} + 32 x^{12} - 36 x^{11} + 51 x^{9} - 167 x^{8} + 153 x^{7} + \cdots + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 101.4 | ||
Root | \(-0.404332 - 1.68420i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2100.101 |
Dual form | 2100.2.bi.m.1601.4 |
$q$-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 \(\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times\).
\(n\) | \(701\) | \(1051\) | \(1177\) | \(1501\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
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 | ||||||||
\(3\) | −0.404332 | + | 1.68420i | −0.233441 | + | 0.972371i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.60761 | + | 2.10133i | −0.607620 | + | 0.794228i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.67303 | − | 1.36195i | −0.891010 | − | 0.453983i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.05856 | − | 1.18851i | −0.620679 | − | 0.358349i | 0.156455 | − | 0.987685i | \(-0.449994\pi\) |
−0.777133 | + | 0.629336i | \(0.783327\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.748179i | 0.207508i | 0.994603 | + | 0.103754i | \(0.0330854\pi\) | ||||
−0.994603 | + | 0.103754i | \(0.966915\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.77242 | − | 6.53402i | 0.914946 | − | 1.58473i | 0.107966 | − | 0.994155i | \(-0.465566\pi\) |
0.806980 | − | 0.590578i | \(-0.201100\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.11872 | + | 3.53264i | −1.40373 | + | 0.810444i | −0.994773 | − | 0.102109i | \(-0.967441\pi\) |
−0.408957 | + | 0.912553i | \(0.634108\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.88904 | − | 3.55717i | −0.630440 | − | 0.776238i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.83006 | − | 1.63394i | 0.590109 | − | 0.340699i | −0.175032 | − | 0.984563i | \(-0.556003\pi\) |
0.765141 | + | 0.643863i | \(0.222669\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.37458 | − | 3.95123i | 0.649439 | − | 0.760414i | ||||
\(28\) | 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 | −0.262313 | − | 0.964983i | \(-0.584485\pi\) |
−0.966856 | + | 0.255322i | \(0.917819\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.83402 | − | 2.98646i | 0.493340 | − | 0.519876i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.15905 | + | 3.73959i | 0.354946 | + | 0.614784i | 0.987109 | − | 0.160051i | \(-0.0511660\pi\) |
−0.632163 | + | 0.774835i | \(0.717833\pi\) | |||||||
\(38\) | 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 | ||||||||
\(43\) | 3.03200 | 0.462375 | 0.231188 | − | 0.972909i | \(-0.425739\pi\) | ||||
0.231188 | + | 0.972909i | \(0.425739\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.22790 | − | 5.59088i | −0.470837 | − | 0.815514i | 0.528606 | − | 0.848867i | \(-0.322715\pi\) |
−0.999444 | + | 0.0333530i | \(0.989381\pi\) | |||||||
\(48\) | 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 | ||||||||
\(53\) | 0.0935472 | + | 0.0540095i | 0.0128497 | + | 0.00741878i | 0.506411 | − | 0.862292i | \(-0.330972\pi\) |
−0.493561 | + | 0.869711i | \(0.664305\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.47567 | − | 11.7335i | −0.460363 | − | 1.55414i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.60248 | + | 11.4358i | −0.859570 | + | 1.48882i | 0.0127699 | + | 0.999918i | \(0.495935\pi\) |
−0.872340 | + | 0.488900i | \(0.837398\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.90005 | − | 3.98375i | 0.883461 | − | 0.510067i | 0.0116632 | − | 0.999932i | \(-0.496287\pi\) |
0.871798 | + | 0.489865i | \(0.162954\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 7.15910 | − | 3.42743i | 0.901962 | − | 0.431816i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.94367 | − | 5.09859i | 0.359627 | − | 0.622892i | −0.628272 | − | 0.777994i | \(-0.716237\pi\) |
0.987898 | + | 0.155102i | \(0.0495707\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.60758 | + | 5.42703i | 0.193530 | + | 0.653338i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 13.9589i | − | 1.65662i | −0.560273 | − | 0.828308i | \(-0.689304\pi\) | ||
0.560273 | − | 0.828308i | \(-0.310696\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.35221 | + | 0.780701i | 0.158265 | + | 0.0913742i | 0.577041 | − | 0.816715i | \(-0.304207\pi\) |
−0.418776 | + | 0.908090i | \(0.637541\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.80681 | − | 2.41505i | 0.661747 | − | 0.275220i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.27644 | − | 2.21086i | −0.143611 | − | 0.248742i | 0.785243 | − | 0.619188i | \(-0.212538\pi\) |
−0.928854 | + | 0.370446i | \(0.879205\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.29018 | + | 7.28107i | 0.587798 | + | 0.809008i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.901948 | 0.0990016 | 0.0495008 | − | 0.998774i | \(-0.484237\pi\) | ||||
0.0495008 | + | 0.998774i | \(0.484237\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.18529 | + | 1.00478i | 0.448710 | + | 0.107724i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.43223 | − | 4.21274i | −0.257816 | − | 0.446550i | 0.707841 | − | 0.706372i | \(-0.249669\pi\) |
−0.965656 | + | 0.259822i | \(0.916336\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.57217 | − | 1.20278i | −0.164808 | − | 0.126086i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 9.42178 | − | 9.92856i | 0.976993 | − | 1.02954i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.9183i | 1.31166i | 0.754909 | + | 0.655829i | \(0.227681\pi\) | ||||
−0.754909 | + | 0.655829i | \(0.772319\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.88390 | + | 5.98057i | 0.390346 | + | 0.601070i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.56718 | − | 2.71443i | 0.155940 | − | 0.270096i | −0.777461 | − | 0.628931i | \(-0.783493\pi\) |
0.933401 | + | 0.358835i | \(0.116826\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −13.6667 | + | 7.89048i | −1.34662 | + | 0.777472i | −0.987769 | − | 0.155922i | \(-0.950165\pi\) |
−0.358852 | + | 0.933394i | \(0.616832\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 11.9952 | − | 6.92544i | 1.15962 | − | 0.669508i | 0.208408 | − | 0.978042i | \(-0.433172\pi\) |
0.951213 | + | 0.308534i | \(0.0998385\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.863166 | − | 1.49505i | 0.0826763 | − | 0.143200i | −0.821722 | − | 0.569888i | \(-0.806987\pi\) |
0.904399 | + | 0.426688i | \(0.140320\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.17117 | + | 2.12423i | −0.680657 | + | 0.201623i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 4.93811i | − | 0.464539i | −0.972652 | − | 0.232269i | \(-0.925385\pi\) | ||
0.972652 | − | 0.232269i | \(-0.0746151\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.01898 | − | 1.99991i | 0.0942050 | − | 0.184891i | ||||
\(118\) | 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 | ||||||||
\(123\) | −4.39359 | + | 18.3009i | −0.396157 | + | 1.65014i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15.9416 | 1.41458 | 0.707292 | − | 0.706921i | \(-0.249917\pi\) | ||||
0.707292 | + | 0.706921i | \(0.249917\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.22593 | + | 5.10648i | −0.107938 | + | 0.449600i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.17025 | − | 7.22309i | −0.364357 | − | 0.631084i | 0.624316 | − | 0.781172i | \(-0.285378\pi\) |
−0.988673 | + | 0.150087i | \(0.952044\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.41328 | − | 18.5366i | 0.209258 | − | 1.60732i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.94718 | − | 4.01096i | −0.593537 | − | 0.342679i | 0.172958 | − | 0.984929i | \(-0.444668\pi\) |
−0.766495 | + | 0.642250i | \(0.778001\pi\) | |||||||
\(138\) | 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 | ||||||||
\(143\) | 0.889218 | − | 1.54017i | 0.0743601 | − | 0.128796i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 12.1192 | − | 0.352278i | 0.999578 | − | 0.0290554i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −15.6215 | + | 9.01906i | −1.27976 | + | 0.738870i | −0.976804 | − | 0.214134i | \(-0.931307\pi\) |
−0.302956 | + | 0.953004i | \(0.597974\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.12850 | − | 3.68667i | 0.173215 | − | 0.300017i | −0.766327 | − | 0.642451i | \(-0.777918\pi\) |
0.939542 | + | 0.342434i | \(0.111251\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −18.9828 | + | 12.3278i | −1.53467 | + | 0.996643i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.4250 | + | 8.32830i | 1.15124 | + | 0.664671i | 0.949190 | − | 0.314703i | \(-0.101905\pi\) |
0.202054 | + | 0.979374i | \(0.435238\pi\) | |||||||
\(158\) | 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 | ||||||||
\(163\) | −8.07999 | − | 13.9950i | −0.632874 | − | 1.09617i | −0.986961 | − | 0.160957i | \(-0.948542\pi\) |
0.354087 | − | 0.935212i | \(-0.384792\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 17.4029 | 1.34668 | 0.673338 | − | 0.739335i | \(-0.264860\pi\) | ||||
0.673338 | + | 0.739335i | \(0.264860\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.4402 | 0.956941 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 21.1668 | − | 1.10948i | 1.61867 | − | 0.0848438i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.83038 | − | 17.0267i | −0.747390 | − | 1.29452i | −0.949070 | − | 0.315066i | \(-0.897973\pi\) |
0.201680 | − | 0.979451i | \(-0.435360\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −16.5906 | − | 15.7437i | −1.24702 | − | 1.18337i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −5.84722 | − | 3.37589i | −0.437042 | − | 0.252326i | 0.265300 | − | 0.964166i | \(-0.414529\pi\) |
−0.702342 | + | 0.711840i | \(0.747862\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 7.71256i | − | 0.573270i | −0.958040 | − | 0.286635i | \(-0.907463\pi\) | ||
0.958040 | − | 0.286635i | \(-0.0925367\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.91950 | + | 13.2318i | 0.289737 | + | 0.978123i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −15.5315 | + | 8.96711i | −1.13577 | + | 0.655740i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.87781 | + | 13.4431i | 0.209330 | + | 0.977845i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −12.7009 | + | 7.33284i | −0.919001 | + | 0.530586i | −0.883316 | − | 0.468777i | \(-0.844695\pi\) |
−0.0356850 | + | 0.999363i | \(0.511361\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.32299 | − | 9.21969i | 0.383157 | − | 0.663648i | −0.608354 | − | 0.793666i | \(-0.708170\pi\) |
0.991512 | + | 0.130018i | \(0.0415034\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 7.53462i | − | 0.536820i | −0.963305 | − | 0.268410i | \(-0.913502\pi\) | ||
0.963305 | − | 0.268410i | \(-0.0864982\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.993782 | + | 0.573760i | 0.0704473 | + | 0.0406728i | 0.534810 | − | 0.844972i | \(-0.320383\pi\) |
−0.464363 | + | 0.885645i | \(0.653717\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7.39680 | + | 7.01924i | 0.521730 | + | 0.495099i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5.22188 | + | 3.99497i | 0.366504 | + | 0.280392i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −9.79018 | + | 0.513161i | −0.680465 | + | 0.0356671i | ||||
\(208\) | 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 | ||||||||
\(213\) | 23.5095 | + | 5.64404i | 1.61085 | + | 0.386723i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 19.3049 | − | 8.02888i | 1.31050 | − | 0.545036i | ||||
\(218\) | 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 | ||||||||
\(223\) | − | 10.6904i | − | 0.715883i | −0.933744 | − | 0.357942i | \(-0.883479\pi\) | ||
0.933744 | − | 0.357942i | \(-0.116521\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −6.69603 | + | 11.5979i | −0.444431 | + | 0.769777i | −0.998012 | − | 0.0630180i | \(-0.979927\pi\) |
0.553581 | + | 0.832795i | \(0.313261\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.32905 | − | 4.80878i | 0.550399 | − | 0.317773i | −0.198884 | − | 0.980023i | \(-0.563732\pi\) |
0.749283 | + | 0.662250i | \(0.230398\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.71953 | + | 10.7563i | 0.113137 | + | 0.707712i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 18.5481 | − | 10.7087i | 1.21512 | − | 0.701552i | 0.251253 | − | 0.967921i | \(-0.419157\pi\) |
0.963871 | + | 0.266369i | \(0.0858240\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4.23964 | − | 1.25586i | 0.275394 | − | 0.0815766i | ||||
\(238\) | 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 | −0.295713 | − | 0.955277i | \(-0.595557\pi\) |
−0.975150 | + | 0.221543i | \(0.928891\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −14.4017 | + | 5.96573i | −0.923872 | + | 0.382702i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.64305 | − | 4.57790i | −0.168173 | − | 0.291285i | ||||
\(248\) | 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 | ||||||||
\(253\) | −7.76780 | −0.488357 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5.92452 | − | 10.2616i | −0.369562 | − | 0.640100i | 0.619935 | − | 0.784653i | \(-0.287159\pi\) |
−0.989497 | + | 0.144553i | \(0.953825\pi\) | |||||||
\(258\) | 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 | ||||||||
\(263\) | 4.79507 | + | 2.76844i | 0.295677 | + | 0.170709i | 0.640499 | − | 0.767959i | \(-0.278727\pi\) |
−0.344822 | + | 0.938668i | \(0.612061\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 8.07851 | − | 2.39300i | 0.494397 | − | 0.146449i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0.504112 | − | 0.873148i | 0.0307363 | − | 0.0532368i | −0.850248 | − | 0.526382i | \(-0.823548\pi\) |
0.880984 | + | 0.473145i | \(0.156881\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.991979 | − | 0.572720i | 0.0602585 | − | 0.0347902i | −0.469568 | − | 0.882896i | \(-0.655590\pi\) |
0.529827 | + | 0.848106i | \(0.322257\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.66140 | − | 2.16152i | 0.161075 | − | 0.130821i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.66672 | + | 8.08299i | −0.280396 | + | 0.485660i | −0.971482 | − | 0.237112i | \(-0.923799\pi\) |
0.691086 | + | 0.722772i | \(0.257132\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 12.9121 | + | 19.8826i | 0.773028 | + | 1.19034i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 0.922818i | − | 0.0550507i | −0.999621 | − | 0.0275253i | \(-0.991237\pi\) | ||
0.999621 | − | 0.0275253i | \(-0.00876270\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.54162 | + | 3.77681i | 0.388859 | + | 0.224508i | 0.681666 | − | 0.731664i | \(-0.261256\pi\) |
−0.292807 | + | 0.956172i | \(0.594589\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −17.4688 | + | 22.8336i | −1.03115 | + | 1.34783i | ||||
\(288\) | 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 | ||||||||
\(293\) | −21.3909 | −1.24967 | −0.624834 | − | 0.780758i | \(-0.714833\pi\) | ||||
−0.624834 | + | 0.780758i | \(0.714833\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −11.6428 | + | 4.12310i | −0.675586 | + | 0.239247i | ||||
\(298\) | 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 | ||||||||
\(303\) | 3.93797 | + | 3.73696i | 0.226230 | + | 0.214683i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 16.7500i | 0.955972i | 0.878368 | + | 0.477986i | \(0.158633\pi\) | ||||
−0.878368 | + | 0.477986i | \(0.841367\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −7.76322 | − | 26.2078i | −0.441634 | − | 1.49091i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.52577 | − | 4.37477i | 0.143224 | − | 0.248070i | −0.785485 | − | 0.618880i | \(-0.787587\pi\) |
0.928709 | + | 0.370810i | \(0.120920\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −12.9998 | + | 7.50546i | −0.734795 | + | 0.424234i | −0.820174 | − | 0.572115i | \(-0.806123\pi\) |
0.0853790 | + | 0.996349i | \(0.472790\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −22.0531 | + | 12.7324i | −1.23863 | + | 0.715121i | −0.968813 | − | 0.247792i | \(-0.920295\pi\) |
−0.269812 | + | 0.962913i | \(0.586962\pi\) | |||||||
\(318\) | 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 | ||||||||
\(323\) | 53.3065i | 2.96605i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.16895 | + | 2.05824i | 0.119943 | + | 0.113821i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 16.9375 | + | 2.20509i | 0.933794 | + | 0.121571i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.45134 | − | 9.44199i | −0.299633 | − | 0.518979i | 0.676419 | − | 0.736517i | \(-0.263531\pi\) |
−0.976052 | + | 0.217538i | \(0.930197\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.678080 | − | 12.9365i | −0.0371585 | − | 0.708918i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −18.4210 | −1.00345 | −0.501727 | − | 0.865026i | \(-0.667302\pi\) | ||||
−0.501727 | + | 0.865026i | \(0.667302\pi\) | |||||||
\(338\) | 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 | ||||||||
\(343\) | 17.1409 | + | 7.01353i | 0.925522 | + | 0.378695i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 8.30010 | + | 4.79206i | 0.445573 | + | 0.257252i | 0.705959 | − | 0.708253i | \(-0.250516\pi\) |
−0.260386 | + | 0.965505i | \(0.583850\pi\) | |||||||
\(348\) | 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 | ||||||||
\(353\) | −9.00574 | + | 15.5984i | −0.479327 | + | 0.830219i | −0.999719 | − | 0.0237089i | \(-0.992453\pi\) |
0.520392 | + | 0.853928i | \(0.325786\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −34.1413 | + | 5.45792i | −1.80695 | + | 0.288864i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3.47735 | − | 2.00765i | 0.183527 | − | 0.105960i | −0.405422 | − | 0.914130i | \(-0.632875\pi\) |
0.588949 | + | 0.808170i | \(0.299542\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.4592 | − | 26.7760i | 0.813640 | − | 1.40927i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 8.88451 | − | 2.63175i | 0.466316 | − | 0.138131i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −29.4897 | − | 17.0259i | −1.53935 | − | 0.888744i | −0.998877 | − | 0.0473832i | \(-0.984912\pi\) |
−0.540473 | − | 0.841361i | \(-0.681755\pi\) | |||||||
\(368\) | 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 | ||||||||
\(373\) | −6.70705 | − | 11.6169i | −0.347278 | − | 0.601503i | 0.638487 | − | 0.769632i | \(-0.279561\pi\) |
−0.985765 | + | 0.168130i | \(0.946227\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.85925 | 0.0957564 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −15.3945 | −0.790764 | −0.395382 | − | 0.918517i | \(-0.629388\pi\) | ||||
−0.395382 | + | 0.918517i | \(0.629388\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6.44569 | + | 26.8487i | −0.330223 | + | 1.37550i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 12.2065 | + | 21.1422i | 0.623722 | + | 1.08032i | 0.988787 | + | 0.149336i | \(0.0477135\pi\) |
−0.365065 | + | 0.930982i | \(0.618953\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −8.10462 | − | 4.12943i | −0.411981 | − | 0.209911i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −30.1938 | − | 17.4324i | −1.53089 | − | 0.883857i | −0.999321 | − | 0.0368391i | \(-0.988271\pi\) |
−0.531564 | − | 0.847018i | \(-0.678396\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 24.6556i | − | 1.24689i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 13.8513 | − | 4.10299i | 0.698704 | − | 0.206969i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 19.5083 | − | 11.2631i | 0.979095 | − | 0.565281i | 0.0770980 | − | 0.997024i | \(-0.475435\pi\) |
0.901997 | + | 0.431743i | \(0.142101\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 30.2434 | + | 11.5594i | 1.51407 | + | 0.578692i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −15.8774 | + | 9.16683i | −0.792881 | + | 0.457770i | −0.840976 | − | 0.541073i | \(-0.818018\pi\) |
0.0480950 | + | 0.998843i | \(0.484685\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.95623 | − | 5.12033i | 0.147260 | − | 0.255062i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 10.2642i | − | 0.508778i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9.37130 | + | 5.41052i | 0.463381 | + | 0.267533i | 0.713465 | − | 0.700691i | \(-0.247125\pi\) |
−0.250084 | + | 0.968224i | \(0.580458\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 9.56420 | − | 10.0786i | 0.471767 | − | 0.497143i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −13.4162 | − | 32.2584i | −0.660169 | − | 1.58733i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 7.77516 | + | 1.86662i | 0.380751 | + | 0.0914086i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 34.1164 | 1.66670 | 0.833348 | − | 0.552749i | \(-0.186421\pi\) | ||||
0.833348 | + | 0.552749i | \(0.186421\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −29.9892 | −1.46158 | −0.730792 | − | 0.682600i | \(-0.760849\pi\) | ||||
−0.730792 | + | 0.682600i | \(0.760849\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.01377 | + | 19.3408i | 0.0492910 | + | 0.940384i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.72144 | + | 20.9036i | −0.131700 | + | 1.01160i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.23441 | + | 2.12036i | 0.107878 | + | 0.102372i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −32.6954 | − | 18.8767i | −1.57488 | − | 0.909258i | −0.995557 | − | 0.0941612i | \(-0.969983\pi\) |
−0.579324 | − | 0.815097i | \(-0.696684\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0.221375i | 0.0106386i | 0.999986 | + | 0.00531930i | \(0.00169319\pi\) | ||||
−0.999986 | + | 0.00531930i | \(0.998307\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −11.5442 | + | 19.9952i | −0.552236 | + | 0.956501i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −12.5292 | + | 7.23374i | −0.597987 | + | 0.345248i | −0.768249 | − | 0.640151i | \(-0.778872\pi\) |
0.170262 | + | 0.985399i | \(0.445538\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4.30690 | + | 20.5536i | −0.205090 | + | 0.978743i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 9.61783 | − | 5.55285i | 0.456957 | − | 0.263824i | −0.253807 | − | 0.967255i | \(-0.581683\pi\) |
0.710764 | + | 0.703431i | \(0.248349\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −8.87359 | − | 29.9563i | −0.419707 | − | 1.41688i | ||||
\(448\) | 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 | ||||||||
\(453\) | 5.34845 | + | 5.07545i | 0.251292 | + | 0.238466i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9.47844 | + | 16.4171i | 0.443383 | + | 0.767962i | 0.997938 | − | 0.0641853i | \(-0.0204449\pi\) |
−0.554555 | + | 0.832147i | \(0.687112\pi\) | |||||||
\(458\) | 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 | ||||||||
\(463\) | −29.3400 | −1.36355 | −0.681773 | − | 0.731564i | \(-0.738791\pi\) | ||||
−0.681773 | + | 0.731564i | \(0.738791\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8.39365 | + | 14.5382i | 0.388412 | + | 0.672749i | 0.992236 | − | 0.124369i | \(-0.0396905\pi\) |
−0.603824 | + | 0.797117i | \(0.706357\pi\) | |||||||
\(468\) | 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 | ||||||||
\(473\) | −6.24154 | − | 3.60356i | −0.286986 | − | 0.165692i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.176496 | − | 0.271776i | −0.00808121 | − | 0.0124438i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.07579 | − | 1.86333i | 0.0491542 | − | 0.0851376i | −0.840401 | − | 0.541964i | \(-0.817681\pi\) |
0.889556 | + | 0.456827i | \(0.151014\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.79788 | + | 1.61536i | −0.127572 | + | 0.0736540i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −13.9884 | − | 5.34650i | −0.636492 | − | 0.243274i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.74460 | − | 3.02174i | 0.0790555 | − | 0.136928i | −0.823787 | − | 0.566899i | \(-0.808143\pi\) |
0.902843 | + | 0.429971i | \(0.141476\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 26.8373 | − | 7.94967i | 1.21362 | − | 0.359497i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 26.1361i | 1.17950i | 0.807584 | + | 0.589752i | \(0.200775\pi\) | ||||
−0.807584 | + | 0.589752i | \(0.799225\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −16.2373 | − | 9.37460i | −0.731290 | − | 0.422211i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 29.3322 | + | 22.4405i | 1.31573 | + | 1.00659i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7.15545 | − | 12.3936i | −0.320322 | − | 0.554814i | 0.660232 | − | 0.751061i | \(-0.270458\pi\) |
−0.980554 | + | 0.196247i | \(0.937124\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −7.03656 | + | 29.3099i | −0.314370 | + | 1.30947i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −39.3226 | −1.75331 | −0.876653 | − | 0.481123i | \(-0.840229\pi\) | ||||
−0.876653 | + | 0.481123i | \(0.840229\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −5.02999 | + | 20.9518i | −0.223390 | + | 0.930501i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −17.4284 | − | 30.1868i | −0.772498 | − | 1.33801i | −0.936190 | − | 0.351495i | \(-0.885674\pi\) |
0.163692 | − | 0.986512i | \(-0.447660\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.81435 | + | 1.58638i | −0.168737 | + | 0.0701774i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −6.68985 | + | 36.0977i | −0.295364 | + | 1.59375i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 15.3455i | 0.674896i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 32.6511 | − | 9.67183i | 1.43322 | − | 0.424546i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −12.3030 | + | 21.3094i | −0.539005 | + | 0.933584i | 0.459953 | + | 0.887943i | \(0.347866\pi\) |
−0.998958 | + | 0.0456406i | \(0.985467\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 23.9603 | − | 13.8335i | 1.04771 | − | 0.604897i | 0.125704 | − | 0.992068i | \(-0.459881\pi\) |
0.922008 | + | 0.387171i | \(0.126548\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −51.6348 | + | 29.8114i | −2.24925 | + | 1.29860i | ||||
\(528\) | 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 | ||||||||
\(533\) | 8.12993i | 0.352146i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 8.04989 | − | 8.48288i | 0.347378 | − | 0.366063i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4.26029 | + | 16.0845i | −0.183504 | + | 0.692808i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.90334 | + | 13.6890i | 0.339791 | + | 0.588536i | 0.984393 | − | 0.175983i | \(-0.0563103\pi\) |
−0.644602 | + | 0.764518i | \(0.722977\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 12.9895 | + | 3.11844i | 0.557431 | + | 0.133825i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 13.9288 | 0.595553 | 0.297776 | − | 0.954636i | \(-0.403755\pi\) | ||||
0.297776 | + | 0.954636i | \(0.403755\pi\) | |||||||
\(548\) | 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 | ||||||||
\(553\) | 6.69778 | + | 0.871984i | 0.284818 | + | 0.0370805i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −29.9559 | − | 17.2950i | −1.26927 | − | 0.732814i | −0.294421 | − | 0.955676i | \(-0.595127\pi\) |
−0.974850 | + | 0.222862i | \(0.928460\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.26848i | 0.0959464i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8.82248 | − | 29.7838i | −0.372485 | − | 1.25747i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 14.4793 | − | 25.0789i | 0.610229 | − | 1.05695i | −0.380972 | − | 0.924586i | \(-0.624411\pi\) |
0.991202 | − | 0.132361i | \(-0.0422560\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −23.8045 | − | 0.588712i | −0.999694 | − | 0.0247236i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −10.1544 | + | 5.86266i | −0.425696 | + | 0.245775i | −0.697511 | − | 0.716574i | \(-0.745709\pi\) |
0.271816 | + | 0.962349i | \(0.412376\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 17.5541 | − | 30.4045i | 0.734614 | − | 1.27239i | −0.220278 | − | 0.975437i | \(-0.570696\pi\) |
0.954892 | − | 0.296952i | \(-0.0959703\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −7.21457 | − | 24.3556i | −0.301393 | − | 1.01747i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −17.3937 | − | 10.0423i | −0.724110 | − | 0.418065i | 0.0921536 | − | 0.995745i | \(-0.470625\pi\) |
−0.816263 | + | 0.577680i | \(0.803958\pi\) | |||||||
\(578\) | 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 | ||||||||
\(583\) | −0.128382 | − | 0.222363i | −0.00531702 | − | 0.00920935i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 32.7111 | 1.35013 | 0.675066 | − | 0.737757i | \(-0.264115\pi\) | ||||
0.675066 | + | 0.737757i | \(0.264115\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 55.8331 | 2.30056 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 12.6898 | + | 3.04649i | 0.521988 | + | 0.125316i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2.23240 | + | 3.86664i | 0.0916738 | + | 0.158784i | 0.908216 | − | 0.418503i | \(-0.137445\pi\) |
−0.816542 | + | 0.577286i | \(0.804112\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.36814 | + | 1.44173i | −0.0559944 | + | 0.0590062i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 31.6126 | + | 18.2515i | 1.29165 | + | 0.745737i | 0.978947 | − | 0.204112i | \(-0.0654308\pi\) |
0.312707 | + | 0.949850i | \(0.398764\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 32.4566i | 1.32393i | 0.749534 | + | 0.661966i | \(0.230278\pi\) | ||||
−0.749534 | + | 0.661966i | \(0.769722\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −14.8125 | + | 9.61955i | −0.603213 | + | 0.391738i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −18.1187 | + | 10.4608i | −0.735416 | + | 0.424593i | −0.820400 | − | 0.571790i | \(-0.806249\pi\) |
0.0849841 | + | 0.996382i | \(0.472916\pi\) | |||||||
\(608\) | 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 | ||||||||
\(613\) | −19.4442 | + | 33.6783i | −0.785343 | + | 1.36025i | 0.143451 | + | 0.989657i | \(0.454180\pi\) |
−0.928794 | + | 0.370596i | \(0.879153\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 12.8874i | − | 0.518828i | −0.965766 | − | 0.259414i | \(-0.916471\pi\) | ||
0.965766 | − | 0.259414i | \(-0.0835294\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.89767 | + | 5.13707i | 0.357628 | + | 0.206476i | 0.668040 | − | 0.744126i | \(-0.267134\pi\) |
−0.310412 | + | 0.950602i | \(0.600467\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.09423 | − | 16.6961i | 0.124167 | − | 0.669990i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 12.7624 | + | 1.66154i | 0.511316 | + | 0.0665683i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −6.79049 | + | 28.2849i | −0.271186 | + | 1.12959i | ||||
\(628\) | 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 | ||||||||
\(633\) | 4.49811 | − | 18.7363i | 0.178784 | − | 0.744701i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.05488 | − | 1.37004i | 0.200282 | − | 0.0542831i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −19.0113 | + | 37.3126i | −0.752076 | + | 1.47606i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 33.7953 | + | 19.5118i | 1.33484 | + | 0.770668i | 0.986036 | − | 0.166529i | \(-0.0532561\pi\) |
0.348799 | + | 0.937197i | \(0.386589\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 12.2206i | 0.481932i | 0.970534 | + | 0.240966i | \(0.0774642\pi\) | ||||
−0.970534 | + | 0.240966i | \(0.922536\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −8.43406 | + | 14.6082i | −0.331577 | + | 0.574308i | −0.982821 | − | 0.184560i | \(-0.940914\pi\) |
0.651244 | + | 0.758868i | \(0.274247\pi\) | |||||||
\(648\) | 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 | ||||||||
\(653\) | 18.7980 | − | 10.8531i | 0.735624 | − | 0.424713i | −0.0848520 | − | 0.996394i | \(-0.527042\pi\) |
0.820476 | + | 0.571681i | \(0.193708\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.55123 | − | 3.92849i | −0.0995331 | − | 0.153265i | ||||
\(658\) | 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 | 0.730944 | − | 0.682438i | \(-0.239080\pi\) |
−0.225537 | + | 0.974235i | \(0.572414\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −6.73018 | + | 7.09219i | −0.261379 | + | 0.275438i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.06039 | − | 7.03281i | −0.157219 | − | 0.272311i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 18.0048 | + | 4.32248i | 0.696104 | + | 0.167117i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −18.9389 | −0.731127 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −0.119232 | −0.00459606 | −0.00229803 | − | 0.999997i | \(-0.500731\pi\) | ||||
−0.00229803 | + | 0.999997i | \(0.500731\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 11.9293 | + | 20.6622i | 0.458482 | + | 0.794114i | 0.998881 | − | 0.0472948i | \(-0.0150600\pi\) |
−0.540399 | + | 0.841409i | \(0.681727\pi\) | |||||||
\(678\) | 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 | ||||||||
\(683\) | 25.3022 | + | 14.6082i | 0.968161 | + | 0.558968i | 0.898675 | − | 0.438615i | \(-0.144531\pi\) |
0.0694856 | + | 0.997583i | \(0.477864\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.73122 | + | 15.9721i | 0.180507 | + | 0.609374i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.0404088 | + | 0.0699901i | −0.00153945 | + | 0.00266641i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −36.0356 | + | 20.8052i | −1.37086 | + | 0.791465i | −0.991036 | − | 0.133594i | \(-0.957348\pi\) |
−0.379822 | + | 0.925059i | \(0.624015\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −18.8110 | − | 1.45309i | −0.714569 | − | 0.0551984i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 40.9922 | − | 71.0005i | 1.55269 | − | 2.68934i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 10.5360 | + | 35.5685i | 0.398509 | + | 1.34532i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 14.6976i | − | 0.555122i | −0.960708 | − | 0.277561i | \(-0.910474\pi\) | ||
0.960708 | − | 0.277561i | \(-0.0895261\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −26.4213 | − | 15.2543i | −0.996497 | − | 0.575328i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.18450 | + | 7.65690i | 0.119765 | + | 0.287967i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 18.6403 | + | 32.2859i | 0.700050 | + | 1.21252i | 0.968448 | + | 0.249214i | \(0.0801723\pi\) |
−0.268398 | + | 0.963308i | \(0.586494\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.400885 | + | 7.64816i | 0.0150343 | + | 0.286828i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −25.8242 | −0.967125 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 42.5776 | + | 10.2218i | 1.59009 | + | 0.381740i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 15.8612 | + | 27.4724i | 0.591522 | + | 1.02455i | 0.994028 | + | 0.109129i | \(0.0348061\pi\) |
−0.402505 | + | 0.915418i | \(0.631861\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.39027 | − | 41.4031i | 0.200744 | − | 1.54193i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 27.1611 | − | 28.6221i | 1.01013 | − | 1.06447i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 30.3126i | 1.12423i | 0.827058 | + | 0.562117i | \(0.190013\pi\) | ||||
−0.827058 | + | 0.562117i | \(0.809987\pi\) | |||||||
\(728\) | 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 | ||||||||
\(733\) | −2.06661 | + | 1.19316i | −0.0763321 | + | 0.0440703i | −0.537680 | − | 0.843149i | \(-0.680699\pi\) |
0.461348 | + | 0.887219i | \(0.347366\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −12.1194 | + | 6.99716i | −0.446425 | + | 0.257744i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.29721 | − | 3.97889i | 0.0845043 | − | 0.146366i | −0.820676 | − | 0.571394i | \(-0.806403\pi\) |
0.905180 | + | 0.425029i | \(0.139736\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 8.77875 | − | 2.60042i | 0.322496 | − | 0.0955289i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 12.5047i | 0.458753i | 0.973338 | + | 0.229376i | \(0.0736687\pi\) | ||||
−0.973338 | + | 0.229376i | \(0.926331\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.41093 | − | 1.22841i | −0.0882114 | − | 0.0449451i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4.73102 | + | 36.3393i | −0.172868 | + | 1.32781i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −17.3708 | − | 30.0872i | −0.633871 | − | 1.09790i | −0.986753 | − | 0.162229i | \(-0.948132\pi\) |
0.352883 | − | 0.935668i | \(-0.385202\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −6.63919 | + | 27.6547i | −0.241946 | + | 1.00779i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 14.5066 | 0.527250 | 0.263625 | − | 0.964625i | \(-0.415082\pi\) | ||||
0.263625 | + | 0.964625i | \(0.415082\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.14077 | − | 13.0825i | 0.114003 | − | 0.474864i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −20.2457 | − | 35.0666i | −0.733906 | − | 1.27116i | −0.955202 | − | 0.295955i | \(-0.904362\pi\) |
0.221296 | − | 0.975207i | \(-0.428971\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.75395 | + | 4.21725i | 0.0634973 | + | 0.152675i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −8.55606 | − | 4.93984i | −0.308941 | − | 0.178367i | ||||
\(768\) | 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 | ||||||||
\(773\) | 2.83006 | − | 4.90181i | 0.101790 | − | 0.176306i | −0.810632 | − | 0.585556i | \(-0.800876\pi\) |
0.912422 | + | 0.409250i | \(0.134210\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 7.06475 | − | 18.4839i | 0.253447 | − | 0.663107i | ||||
\(778\) | 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 | ||||||||
\(783\) | −9.81894 | − | 8.38596i | −0.350900 | − | 0.299690i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.76237 | − | 1.59485i | −0.0984677 | − | 0.0568504i | 0.449958 | − | 0.893050i | \(-0.351439\pi\) |
−0.548425 | + | 0.836200i | \(0.684772\pi\) | |||||||
\(788\) | 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 | ||||||||
\(793\) | 2.98056 | + | 5.16248i | 0.105843 | + | 0.183325i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 18.7853 | 0.665410 | 0.332705 | − | 0.943031i | \(-0.392039\pi\) | ||||
0.332705 | + | 0.943031i | \(0.392039\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −48.7079 | −1.72316 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.763875 | + | 14.5734i | 0.0269902 | + | 0.514924i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.85574 | − | 3.21424i | −0.0654877 | − | 0.113428i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.26672 | + | 1.20207i | 0.0445908 | + | 0.0423147i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −24.5995 | − | 14.2025i | −0.864873 | − | 0.499335i | 0.000767968 | − | 1.00000i | \(-0.499756\pi\) |
−0.865641 | + | 0.500665i | \(0.833089\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 46.9628i | 1.64909i | 0.565799 | + | 0.824543i | \(0.308568\pi\) | ||||
−0.565799 | + | 0.824543i | \(0.691432\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0.563482 | + | 1.90226i | 0.0197622 | + | 0.0667151i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −18.5519 | + | 10.7110i | −0.649050 | + | 0.374729i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.56433 | + | 5.35629i | 0.0896050 | + | 0.187164i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 16.9019 | − | 9.75831i | 0.589880 | − | 0.340567i | −0.175170 | − | 0.984538i | \(-0.556048\pi\) |
0.765050 | + | 0.643971i | \(0.222714\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 12.5304 | − | 21.7033i | 0.436782 | − | 0.756529i | −0.560657 | − | 0.828048i | \(-0.689451\pi\) |
0.997439 | + | 0.0715193i | \(0.0227848\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 40.2141i | − | 1.39838i | −0.714935 | − | 0.699191i | \(-0.753544\pi\) | ||
0.714935 | − | 0.699191i | \(-0.246456\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5.52711 | + | 3.19108i | 0.191964 | + | 0.110831i | 0.592902 | − | 0.805275i | \(-0.297982\pi\) |
−0.400937 | + | 0.916105i | \(0.631316\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −11.7264 | − | 11.1279i | −0.406785 | − | 0.386022i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −51.0534 | − | 13.5225i | −1.76889 | − | 0.468526i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −38.7069 | + | 13.7074i | −1.33791 | + | 0.473796i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 15.2513 | 0.526534 | 0.263267 | − | 0.964723i | \(-0.415200\pi\) | ||||
0.263267 | + | 0.964723i | \(0.415200\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 22.8246 | 0.787055 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.55421 | + | 0.373125i | 0.0535297 | + | 0.0128511i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 14.0358 | + | 1.82732i | 0.482274 | + | 0.0627873i | ||||
\(848\) | 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 | ||||||||
\(853\) | − | 16.7815i | − | 0.574586i | −0.957843 | − | 0.287293i | \(-0.907245\pi\) | ||
0.957843 | − | 0.287293i | \(-0.0927554\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 9.68551 | − | 16.7758i | 0.330851 | − | 0.573050i | −0.651828 | − | 0.758367i | \(-0.725998\pi\) |
0.982679 | + | 0.185317i | \(0.0593311\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 42.4714 | − | 24.5208i | 1.44910 | − | 0.836641i | 0.450676 | − | 0.892688i | \(-0.351183\pi\) |
0.998428 | + | 0.0560471i | \(0.0178497\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −31.3931 | − | 38.6532i | −1.06987 | − | 1.31730i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −19.4609 | + | 11.2358i | −0.662458 | + | 0.382470i | −0.793213 | − | 0.608944i | \(-0.791593\pi\) |
0.130755 | + | 0.991415i | \(0.458260\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 66.3036 | − | 19.6403i | 2.25179 | − | 0.667020i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6.06826i | 0.205851i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.81466 | + | 2.20239i | 0.129255 | + | 0.0746253i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 17.5941 | − | 34.5311i | 0.595471 | − | 1.16870i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −15.5087 | − | 26.8618i | −0.523691 | − | 0.907059i | −0.999620 | − | 0.0275755i | \(-0.991221\pi\) |
0.475929 | − | 0.879484i | \(-0.342112\pi\) | |||||||
\(878\) | 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 | ||||||||
\(883\) | 34.3430 | 1.15573 | 0.577867 | − | 0.816131i | \(-0.303885\pi\) | ||||
0.577867 | + | 0.816131i | \(0.303885\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −27.9903 | − | 48.4807i | −0.939824 | − | 1.62782i | −0.765797 | − | 0.643082i | \(-0.777655\pi\) |
−0.174027 | − | 0.984741i | \(-0.555678\pi\) | |||||||
\(888\) | 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 | ||||||||
\(893\) | 39.5012 | + | 22.8060i | 1.32186 | + | 0.763175i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −4.06039 | + | 1.20276i | −0.135573 | + | 0.0401590i | ||||
\(898\) | 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 | ||||||||
\(903\) | −8.75956 | − | 10.7853i | −0.291500 | − | 0.358913i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0.494450 | − | 0.856413i | 0.0164180 | − | 0.0284367i | −0.857700 | − | 0.514151i | \(-0.828107\pi\) |
0.874118 | + | 0.485714i | \(0.161440\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −7.88602 | + | 5.12133i | −0.261563 | + | 0.169864i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 28.5096i | − | 0.944567i | −0.881447 | − | 0.472283i | \(-0.843430\pi\) | ||
0.881447 | − | 0.472283i | \(-0.156570\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.85671 | − | 1.07197i | −0.0614482 | − | 0.0354771i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 21.8822 | + | 2.84885i | 0.722615 | + | 0.0940774i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.40350 | + | 2.43093i | 0.0462971 | + | 0.0801889i | 0.888245 | − | 0.459369i | \(-0.151925\pi\) |
−0.841948 | + | 0.539558i | \(0.818591\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −28.2102 | − | 6.77256i | −0.929559 | − | 0.223163i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 10.4438 | 0.343761 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 47.2780 | − | 2.47812i | 1.55281 | − | 0.0813920i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −6.57702 | − | 11.3917i | −0.215785 | − | 0.373751i | 0.737730 | − | 0.675096i | \(-0.235898\pi\) |
−0.953515 | + | 0.301345i | \(0.902564\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 35.0718 | + | 34.8707i | 1.14943 | + | 1.14284i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 6.34672 | + | 6.02276i | 0.207782 | + | 0.197176i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 20.2219i | 0.660622i | 0.943872 | + | 0.330311i | \(0.107154\pi\) | ||||
−0.943872 | + | 0.330311i | \(0.892846\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −7.38441 | − | 24.9290i | −0.240981 | − | 0.813527i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −22.8119 | + | 39.5113i | −0.743646 | + | 1.28803i | 0.207179 | + | 0.978303i | \(0.433572\pi\) |
−0.950825 | + | 0.309729i | \(0.899762\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 30.7523 | − | 17.7548i | 1.00143 | − | 0.578177i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 50.7421 | − | 29.2959i | 1.64890 | − | 0.951990i | 0.671383 | − | 0.741110i | \(-0.265700\pi\) |
0.977512 | − | 0.210880i | \(-0.0676329\pi\) | |||||||
\(948\) | 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 | ||||||||
\(953\) | − | 26.9224i | − | 0.872101i | −0.899922 | − | 0.436051i | \(-0.856377\pi\) | ||
0.899922 | − | 0.436051i | \(-0.143623\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −7.42147 | − | 7.04265i | −0.239902 | − | 0.227657i | ||||
\(958\) | 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 | ||||||||
\(963\) | −41.4957 | + | 2.17503i | −1.33718 | + | 0.0700894i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −17.4008 | −0.559572 | −0.279786 | − | 0.960062i | \(-0.590263\pi\) | ||||
−0.279786 | + | 0.960062i | \(0.590263\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −89.7785 | − | 21.5535i | −2.88410 | − | 0.692399i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −12.6200 | − | 21.8585i | −0.404996 | − | 0.701474i | 0.589325 | − | 0.807896i | \(-0.299394\pi\) |
−0.994321 | + | 0.106422i | \(0.966060\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 9.70087 | + | 7.42160i | 0.310996 | + | 0.237926i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 6.49450 | + | 3.74960i | 0.207778 | + | 0.119960i | 0.600278 | − | 0.799791i | \(-0.295057\pi\) |
−0.392501 | + | 0.919752i | \(0.628390\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 11.5629i | 0.369552i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.34345 | + | 2.82072i | −0.138676 | + | 0.0900586i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 12.9037 | − | 22.3498i | 0.411563 | − | 0.712848i | −0.583498 | − | 0.812115i | \(-0.698316\pi\) |
0.995061 | + | 0.0992666i | \(0.0316497\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −10.5622 | + | 27.6345i | −0.336198 | + | 0.879615i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 8.58074 | − | 4.95409i | 0.272852 | − | 0.157531i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −11.4009 | + | 19.7469i | −0.362161 | + | 0.627280i | −0.988316 | − | 0.152418i | \(-0.951294\pi\) |
0.626156 | + | 0.779698i | \(0.284627\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 18.1063 | − | 5.36341i | 0.574586 | − | 0.170203i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −10.2479 | − | 5.91662i | −0.324554 | − | 0.187381i | 0.328867 | − | 0.944376i | \(-0.393333\pi\) |
−0.653421 | + | 0.756995i | \(0.726667\pi\) | |||||||
\(998\) | 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.bi.m.101.4 | yes | 16 | |
3.2 | odd | 2 | inner | 2100.2.bi.m.101.7 | yes | 16 | |
5.2 | odd | 4 | 2100.2.bo.i.1949.16 | 32 | |||
5.3 | odd | 4 | 2100.2.bo.i.1949.1 | 32 | |||
5.4 | even | 2 | 2100.2.bi.l.101.5 | yes | 16 | ||
7.5 | odd | 6 | inner | 2100.2.bi.m.1601.7 | yes | 16 | |
15.2 | even | 4 | 2100.2.bo.i.1949.6 | 32 | |||
15.8 | even | 4 | 2100.2.bo.i.1949.11 | 32 | |||
15.14 | odd | 2 | 2100.2.bi.l.101.2 | ✓ | 16 | ||
21.5 | even | 6 | inner | 2100.2.bi.m.1601.4 | yes | 16 | |
35.12 | even | 12 | 2100.2.bo.i.1349.11 | 32 | |||
35.19 | odd | 6 | 2100.2.bi.l.1601.2 | yes | 16 | ||
35.33 | even | 12 | 2100.2.bo.i.1349.6 | 32 | |||
105.47 | odd | 12 | 2100.2.bo.i.1349.1 | 32 | |||
105.68 | odd | 12 | 2100.2.bo.i.1349.16 | 32 | |||
105.89 | even | 6 | 2100.2.bi.l.1601.5 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2100.2.bi.l.101.2 | ✓ | 16 | 15.14 | odd | 2 | ||
2100.2.bi.l.101.5 | yes | 16 | 5.4 | even | 2 | ||
2100.2.bi.l.1601.2 | yes | 16 | 35.19 | odd | 6 | ||
2100.2.bi.l.1601.5 | yes | 16 | 105.89 | even | 6 | ||
2100.2.bi.m.101.4 | yes | 16 | 1.1 | even | 1 | trivial | |
2100.2.bi.m.101.7 | yes | 16 | 3.2 | odd | 2 | inner | |
2100.2.bi.m.1601.4 | yes | 16 | 21.5 | even | 6 | inner | |
2100.2.bi.m.1601.7 | yes | 16 | 7.5 | odd | 6 | inner | |
2100.2.bo.i.1349.1 | 32 | 105.47 | odd | 12 | |||
2100.2.bo.i.1349.6 | 32 | 35.33 | even | 12 | |||
2100.2.bo.i.1349.11 | 32 | 35.12 | even | 12 | |||
2100.2.bo.i.1349.16 | 32 | 105.68 | odd | 12 | |||
2100.2.bo.i.1949.1 | 32 | 5.3 | odd | 4 | |||
2100.2.bo.i.1949.6 | 32 | 15.2 | even | 4 | |||
2100.2.bo.i.1949.11 | 32 | 15.8 | even | 4 | |||
2100.2.bo.i.1949.16 | 32 | 5.2 | odd | 4 |