Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2240,2,Mod(1791,2240)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2240, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 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("2240.1791");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2240 = 2^{6} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2240.k (of order \(2\), degree \(1\), 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: | \(17.8864900528\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4 x^{15} - 6 x^{14} + 68 x^{13} - 126 x^{12} - 148 x^{11} + 1006 x^{10} - 1516 x^{9} + \cdots + 5956 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{11} \) |
Twist minimal: | no (minimal twist has level 1120) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1791.1 | ||
Root | \(1.08568 - 1.64772i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2240.1791 |
Dual form | 2240.2.k.g.1791.2 |
$q$-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 \(\left(\mathbb{Z}/2240\mathbb{Z}\right)^\times\).
\(n\) | \(897\) | \(1471\) | \(1541\) | \(1921\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −3.29545 | −1.90263 | −0.951314 | − | 0.308223i | \(-0.900266\pi\) | ||||
−0.951314 | + | 0.308223i | \(0.900266\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 1.00000i | − | 0.447214i | ||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.01507 | − | 1.71449i | 0.761626 | − | 0.648017i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 7.85998 | 2.61999 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 1.43526i | − | 0.432748i | −0.976311 | − | 0.216374i | \(-0.930577\pi\) | ||
0.976311 | − | 0.216374i | \(-0.0694230\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.60035i | 1.55326i | 0.629958 | + | 0.776629i | \(0.283072\pi\) | ||||
−0.629958 | + | 0.776629i | \(0.716928\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.29545i | 0.850881i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.85877i | 0.450819i | 0.974264 | + | 0.225410i | \(0.0723720\pi\) | ||||
−0.974264 | + | 0.225410i | \(0.927628\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.04101 | 0.697656 | 0.348828 | − | 0.937187i | \(-0.386580\pi\) | ||||
0.348828 | + | 0.937187i | \(0.386580\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −6.64057 | + | 5.65002i | −1.44909 | + | 1.23294i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.989130i | 0.206248i | 0.994669 | + | 0.103124i | \(0.0328838\pi\) | ||||
−0.994669 | + | 0.103124i | \(0.967116\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −16.0158 | −3.08225 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.89054 | 1.09385 | 0.546923 | − | 0.837183i | \(-0.315799\pi\) | ||||
0.546923 | + | 0.837183i | \(0.315799\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.82964 | −1.40624 | −0.703122 | − | 0.711069i | \(-0.748211\pi\) | ||||
−0.703122 | + | 0.711069i | \(0.748211\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.72983i | 0.823358i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.71449 | − | 2.01507i | −0.289802 | − | 0.340609i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.93243 | 0.646487 | 0.323244 | − | 0.946316i | \(-0.395227\pi\) | ||||
0.323244 | + | 0.946316i | \(0.395227\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 18.4557i | − | 2.95527i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.37831i | 1.30847i | 0.756290 | + | 0.654236i | \(0.227010\pi\) | ||||
−0.756290 | + | 0.654236i | \(0.772990\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 0.890743i | − | 0.135837i | −0.997691 | − | 0.0679185i | \(-0.978364\pi\) | ||
0.997691 | − | 0.0679185i | \(-0.0216358\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − | 7.85998i | − | 1.17170i | ||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.347743 | −0.0507236 | −0.0253618 | − | 0.999678i | \(-0.508074\pi\) | ||||
−0.0253618 | + | 0.999678i | \(0.508074\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.12103 | − | 6.90965i | 0.160147 | − | 0.987093i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 6.12550i | − | 0.857741i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −12.1711 | −1.67183 | −0.835915 | − | 0.548859i | \(-0.815062\pi\) | ||||
−0.835915 | + | 0.548859i | \(0.815062\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.43526 | −0.193531 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −10.0215 | −1.32738 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.32153 | −0.562616 | −0.281308 | − | 0.959618i | \(-0.590768\pi\) | ||||
−0.281308 | + | 0.959618i | \(0.590768\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 13.2238i | − | 1.69314i | −0.532280 | − | 0.846568i | \(-0.678665\pi\) | ||
0.532280 | − | 0.846568i | \(-0.321335\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 15.8384 | − | 13.4759i | 1.99545 | − | 1.69780i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 5.60035 | 0.694639 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 15.3113i | 1.87057i | 0.353895 | + | 0.935285i | \(0.384857\pi\) | ||||
−0.353895 | + | 0.935285i | \(0.615143\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 3.25963i | − | 0.392413i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.574410i | 0.0681700i | 0.999419 | + | 0.0340850i | \(0.0108517\pi\) | ||||
−0.999419 | + | 0.0340850i | \(0.989148\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 13.6466i | 1.59721i | 0.601854 | + | 0.798606i | \(0.294429\pi\) | ||||
−0.601854 | + | 0.798606i | \(0.705571\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.29545 | 0.380526 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.46075 | − | 2.89216i | −0.280428 | − | 0.329592i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.17455i | 0.357165i | 0.983925 | + | 0.178582i | \(0.0571511\pi\) | ||||
−0.983925 | + | 0.178582i | \(0.942849\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 29.1994 | 3.24438 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.59090 | 0.833210 | 0.416605 | − | 0.909088i | \(-0.363220\pi\) | ||||
0.416605 | + | 0.909088i | \(0.363220\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.85877 | 0.201612 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −19.4120 | −2.08118 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.08220i | 0.856711i | 0.903610 | + | 0.428356i | \(0.140907\pi\) | ||||
−0.903610 | + | 0.428356i | \(0.859093\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 9.60177 | + | 11.2851i | 1.00654 | + | 1.18300i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 25.8022 | 2.67556 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 3.04101i | − | 0.312001i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 4.66048i | − | 0.473200i | −0.971607 | − | 0.236600i | \(-0.923967\pi\) | ||
0.971607 | − | 0.236600i | \(-0.0760332\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 11.2811i | − | 1.13380i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.482485i | 0.0480090i | 0.999712 | + | 0.0240045i | \(0.00764161\pi\) | ||||
−0.999712 | + | 0.0240045i | \(0.992358\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.52386 | 0.839880 | 0.419940 | − | 0.907552i | \(-0.362051\pi\) | ||||
0.419940 | + | 0.907552i | \(0.362051\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 5.65002 | + | 6.64057i | 0.551386 | + | 0.648053i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 15.2510i | 1.47437i | 0.675692 | + | 0.737184i | \(0.263845\pi\) | ||||
−0.675692 | + | 0.737184i | \(0.736155\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 17.8125 | 1.70613 | 0.853066 | − | 0.521804i | \(-0.174741\pi\) | ||||
0.853066 | + | 0.521804i | \(0.174741\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −12.9591 | −1.23002 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −17.7201 | −1.66697 | −0.833485 | − | 0.552542i | \(-0.813658\pi\) | ||||
−0.833485 | + | 0.552542i | \(0.813658\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.989130 | 0.0922369 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 44.0187i | 4.06953i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.18686 | + | 3.74556i | 0.292139 | + | 0.343355i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.94002 | 0.812729 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 27.6103i | − | 2.48954i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.21856i | 0.551808i | 0.961185 | + | 0.275904i | \(0.0889771\pi\) | ||||
−0.961185 | + | 0.275904i | \(0.911023\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.93540i | 0.258447i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.28635 | −0.461870 | −0.230935 | − | 0.972969i | \(-0.574179\pi\) | ||||
−0.230935 | + | 0.972969i | \(0.574179\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.12786 | − | 5.21380i | 0.531353 | − | 0.452093i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 16.0158i | 1.37842i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 7.48277 | 0.639297 | 0.319648 | − | 0.947536i | \(-0.396435\pi\) | ||||
0.319648 | + | 0.947536i | \(0.396435\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 13.9691 | 1.18484 | 0.592421 | − | 0.805629i | \(-0.298172\pi\) | ||||
0.592421 | + | 0.805629i | \(0.298172\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.14597 | 0.0965081 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 8.03797 | 0.672169 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 5.89054i | − | 0.489183i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3.69429 | + | 22.7704i | −0.304700 | + | 1.87807i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −0.118251 | −0.00968748 | −0.00484374 | − | 0.999988i | \(-0.501542\pi\) | ||||
−0.00484374 | + | 0.999988i | \(0.501542\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.2429i | 0.996315i | 0.867087 | + | 0.498158i | \(0.165990\pi\) | ||||
−0.867087 | + | 0.498158i | \(0.834010\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 14.6099i | 1.18114i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 7.82964i | 0.628892i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.60455i | 0.447292i | 0.974670 | + | 0.223646i | \(0.0717959\pi\) | ||||
−0.974670 | + | 0.223646i | \(0.928204\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 40.1092 | 3.18087 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.69586 | + | 1.99317i | 0.133652 | + | 0.157084i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.0820i | 0.868012i | 0.900910 | + | 0.434006i | \(0.142900\pi\) | ||||
−0.900910 | + | 0.434006i | \(0.857100\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 4.72983 | 0.368217 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.22069 | −0.171842 | −0.0859212 | − | 0.996302i | \(-0.527383\pi\) | ||||
−0.0859212 | + | 0.996302i | \(0.527383\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −18.3640 | −1.41261 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 23.9023 | 1.82786 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 13.3236i | − | 1.01297i | −0.862248 | − | 0.506486i | \(-0.830944\pi\) | ||
0.862248 | − | 0.506486i | \(-0.169056\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.01507 | + | 1.71449i | −0.152325 | + | 0.129603i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 14.2414 | 1.07045 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 25.6905i | 1.92020i | 0.279658 | + | 0.960100i | \(0.409779\pi\) | ||||
−0.279658 | + | 0.960100i | \(0.590221\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.87811i | 0.213928i | 0.994263 | + | 0.106964i | \(0.0341130\pi\) | ||||
−0.994263 | + | 0.106964i | \(0.965887\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 43.5784i | 3.22141i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 3.93243i | − | 0.289118i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.66783 | 0.195091 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −32.2730 | + | 27.4590i | −2.34752 | + | 1.99735i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 16.9335i | − | 1.22526i | −0.790369 | − | 0.612632i | \(-0.790111\pi\) | ||
0.790369 | − | 0.612632i | \(-0.209889\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 18.4434 | 1.32759 | 0.663794 | − | 0.747915i | \(-0.268945\pi\) | ||||
0.663794 | + | 0.747915i | \(0.268945\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −18.4557 | −1.32164 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.64444 | −0.473396 | −0.236698 | − | 0.971583i | \(-0.576065\pi\) | ||||
−0.236698 | + | 0.971583i | \(0.576065\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 15.0193 | 1.06469 | 0.532345 | − | 0.846527i | \(-0.321311\pi\) | ||||
0.532345 | + | 0.846527i | \(0.321311\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 50.4575i | − | 3.55900i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 11.8699 | − | 10.0993i | 0.833101 | − | 0.708831i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8.37831 | 0.585167 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 7.77455i | 0.540369i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 4.36465i | − | 0.301909i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 22.4412i | − | 1.54492i | −0.635066 | − | 0.772458i | \(-0.719027\pi\) | ||
0.635066 | − | 0.772458i | \(-0.280973\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 1.89294i | − | 0.129702i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.890743 | −0.0607481 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −15.7773 | + | 13.4239i | −1.07103 | + | 0.911271i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 44.9717i | − | 3.03890i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −10.4098 | −0.700239 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.57577 | −0.172486 | −0.0862432 | − | 0.996274i | \(-0.527486\pi\) | ||||
−0.0862432 | + | 0.996274i | \(0.527486\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −7.85998 | −0.523999 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 11.4113 | 0.757393 | 0.378696 | − | 0.925521i | \(-0.376372\pi\) | ||||
0.378696 | + | 0.925521i | \(0.376372\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 20.3747i | 1.34640i | 0.739462 | + | 0.673198i | \(0.235080\pi\) | ||||
−0.739462 | + | 0.673198i | \(0.764920\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 8.10926 | + | 9.53095i | 0.533550 | + | 0.627090i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3.46425 | 0.226950 | 0.113475 | − | 0.993541i | \(-0.463802\pi\) | ||||
0.113475 | + | 0.993541i | \(0.463802\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.347743i | 0.0226843i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 10.4616i | − | 0.679552i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 16.0893i | − | 1.04073i | −0.853944 | − | 0.520364i | \(-0.825796\pi\) | ||
0.853944 | − | 0.520364i | \(-0.174204\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.45521i | 0.351401i | 0.984444 | + | 0.175701i | \(0.0562191\pi\) | ||||
−0.984444 | + | 0.175701i | \(0.943781\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −48.1776 | −3.09060 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −6.90965 | − | 1.12103i | −0.441441 | − | 0.0716199i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 17.0308i | 1.08364i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −25.0154 | −1.58529 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 19.1058 | 1.20595 | 0.602975 | − | 0.797760i | \(-0.293982\pi\) | ||||
0.602975 | + | 0.797760i | \(0.293982\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.41966 | 0.0892533 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −6.12550 | −0.383593 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 10.7668i | − | 0.671612i | −0.941931 | − | 0.335806i | \(-0.890991\pi\) | ||
0.941931 | − | 0.335806i | \(-0.109009\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.92412 | − | 6.74212i | 0.492381 | − | 0.418935i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 46.2995 | 2.86587 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 10.7609i | − | 0.663545i | −0.943359 | − | 0.331773i | \(-0.892353\pi\) | ||
0.943359 | − | 0.331773i | \(-0.107647\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 12.1711i | 0.747665i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 26.6345i | − | 1.63000i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 17.9573i | − | 1.09488i | −0.836846 | − | 0.547439i | \(-0.815603\pi\) | ||
0.836846 | − | 0.547439i | \(-0.184397\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −16.5637 | −1.00617 | −0.503085 | − | 0.864237i | \(-0.667802\pi\) | ||||
−0.503085 | + | 0.864237i | \(0.667802\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −31.6421 | − | 37.1895i | −1.91507 | − | 2.25081i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.43526i | 0.0865495i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.37156 | −0.442914 | −0.221457 | − | 0.975170i | \(-0.571081\pi\) | ||||
−0.221457 | + | 0.975170i | \(0.571081\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −61.5408 | −3.68435 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.12029 | −0.544071 | −0.272035 | − | 0.962287i | \(-0.587697\pi\) | ||||
−0.272035 | + | 0.962287i | \(0.587697\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 27.4579 | 1.63221 | 0.816103 | − | 0.577907i | \(-0.196130\pi\) | ||||
0.816103 | + | 0.577907i | \(0.196130\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 10.0215i | 0.593623i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 14.3646 | + | 16.8829i | 0.847913 | + | 0.996566i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13.5450 | 0.796762 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 15.3584i | 0.900324i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 22.5135i | − | 1.31525i | −0.753345 | − | 0.657625i | \(-0.771561\pi\) | ||
0.753345 | − | 0.657625i | \(-0.228439\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.32153i | 0.251609i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 22.9869i | 1.33384i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −5.53948 | −0.320356 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.52717 | − | 1.79491i | −0.0880247 | − | 0.103457i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 1.59000i | − | 0.0913433i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −13.2238 | −0.757194 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −11.3657 | −0.648677 | −0.324339 | − | 0.945941i | \(-0.605142\pi\) | ||||
−0.324339 | + | 0.945941i | \(0.605142\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −28.0899 | −1.59798 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 14.5545 | 0.825309 | 0.412654 | − | 0.910888i | \(-0.364602\pi\) | ||||
0.412654 | + | 0.910888i | \(0.364602\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 7.75419i | − | 0.438292i | −0.975692 | − | 0.219146i | \(-0.929673\pi\) | ||
0.975692 | − | 0.219146i | \(-0.0703272\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −13.4759 | − | 15.8384i | −0.759280 | − | 0.892395i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 9.31447 | 0.523153 | 0.261577 | − | 0.965183i | \(-0.415758\pi\) | ||||
0.261577 | + | 0.965183i | \(0.415758\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 8.45446i | − | 0.473359i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 50.2589i | − | 2.80518i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.65256i | 0.314517i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 5.60035i | − | 0.310652i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −58.7003 | −3.24613 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.700728 | + | 0.596203i | −0.0386324 | + | 0.0328698i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 22.9879i | 1.26353i | 0.775161 | + | 0.631764i | \(0.217669\pi\) | ||||
−0.775161 | + | 0.631764i | \(0.782331\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 30.9088 | 1.69379 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 15.3113 | 0.836544 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.17653 | 0.336457 | 0.168228 | − | 0.985748i | \(-0.446195\pi\) | ||||
0.168228 | + | 0.985748i | \(0.446195\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 58.3958 | 3.17163 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 11.2376i | 0.608549i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −9.58759 | − | 15.8454i | −0.517681 | − | 0.855573i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3.25963 | −0.175493 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 9.47042i | 0.508399i | 0.967152 | + | 0.254199i | \(0.0818119\pi\) | ||||
−0.967152 | + | 0.254199i | \(0.918188\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 22.5004i | 1.20442i | 0.798339 | + | 0.602209i | \(0.205712\pi\) | ||||
−0.798339 | + | 0.602209i | \(0.794288\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 89.6943i | − | 4.78753i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 27.2798i | 1.45196i | 0.687717 | + | 0.725979i | \(0.258613\pi\) | ||||
−0.687717 | + | 0.725979i | \(0.741387\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.574410 | 0.0304865 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −10.5021 | − | 12.3433i | −0.555831 | − | 0.653278i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 15.4879i | − | 0.817421i | −0.912664 | − | 0.408711i | \(-0.865979\pi\) | ||
0.912664 | − | 0.408711i | \(-0.134021\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.75224 | −0.513276 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −29.4614 | −1.54632 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 13.6466 | 0.714295 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.442314 | 0.0230886 | 0.0115443 | − | 0.999933i | \(-0.496325\pi\) | ||||
0.0115443 | + | 0.999933i | \(0.496325\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 65.8534i | 3.42819i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −24.5256 | + | 20.8673i | −1.27331 | + | 1.08337i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.61184 | −0.0834581 | −0.0417291 | − | 0.999129i | \(-0.513287\pi\) | ||||
−0.0417291 | + | 0.999129i | \(0.513287\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 3.29545i | − | 0.170176i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 32.9891i | 1.69903i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.5583i | 0.747811i | 0.927467 | + | 0.373905i | \(0.121982\pi\) | ||||
−0.927467 | + | 0.373905i | \(0.878018\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 20.4929i | − | 1.04989i | ||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −5.85765 | −0.299312 | −0.149656 | − | 0.988738i | \(-0.547817\pi\) | ||||
−0.149656 | + | 0.988738i | \(0.547817\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.89216 | + | 2.46075i | −0.147398 | + | 0.125411i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 7.00122i | − | 0.355892i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −0.672103 | −0.0340770 | −0.0170385 | − | 0.999855i | \(-0.505424\pi\) | ||||
−0.0170385 | + | 0.999855i | \(0.505424\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.83857 | −0.0929805 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 17.4209 | 0.878768 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.17455 | 0.159729 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 4.62099i | − | 0.231921i | −0.993254 | − | 0.115960i | \(-0.963005\pi\) | ||
0.993254 | − | 0.115960i | \(-0.0369945\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −20.1941 | + | 17.1818i | −1.01097 | + | 0.860166i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 29.8603 | 1.49115 | 0.745576 | − | 0.666421i | \(-0.232175\pi\) | ||||
0.745576 | + | 0.666421i | \(0.232175\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 43.8487i | − | 2.18426i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 29.1994i | − | 1.45093i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 5.64406i | − | 0.279766i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 9.08811i | − | 0.449378i | −0.974431 | − | 0.224689i | \(-0.927863\pi\) | ||
0.974431 | − | 0.224689i | \(-0.0721366\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −24.6591 | −1.21634 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −8.70820 | + | 7.40924i | −0.428502 | + | 0.364585i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 7.59090i | − | 0.372623i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −46.0344 | −2.25431 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −27.1192 | −1.32486 | −0.662430 | − | 0.749124i | \(-0.730475\pi\) | ||||
−0.662430 | + | 0.749124i | \(0.730475\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.7788 | 0.671537 | 0.335768 | − | 0.941945i | \(-0.391004\pi\) | ||||
0.335768 | + | 0.941945i | \(0.391004\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.73326 | −0.132895 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 1.85877i | − | 0.0901638i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −22.6721 | − | 26.6469i | −1.09718 | − | 1.28954i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −26.4887 | −1.27889 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 29.3812i | 1.41524i | 0.706591 | + | 0.707622i | \(0.250232\pi\) | ||||
−0.706591 | + | 0.707622i | \(0.749768\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.04892i | 0.242636i | 0.992614 | + | 0.121318i | \(0.0387120\pi\) | ||||
−0.992614 | + | 0.121318i | \(0.961288\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 19.4120i | 0.930733i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.00796i | 0.143890i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10.2167 | 0.487617 | 0.243808 | − | 0.969823i | \(-0.421603\pi\) | ||||
0.243808 | + | 0.969823i | \(0.421603\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 8.81127 | − | 54.3098i | 0.419584 | − | 2.58618i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 9.75208i | − | 0.463335i | −0.972795 | − | 0.231668i | \(-0.925582\pi\) | ||
0.972795 | − | 0.231668i | \(-0.0744182\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 8.08220 | 0.383133 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0.389689 | 0.0184317 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0.478289 | 0.0225719 | 0.0112859 | − | 0.999936i | \(-0.496407\pi\) | ||||
0.0112859 | + | 0.999936i | \(0.496407\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 12.0251 | 0.566238 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 40.3459i | − | 1.89562i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 11.2851 | − | 9.60177i | 0.529054 | − | 0.450138i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.01299 | −0.0473855 | −0.0236928 | − | 0.999719i | \(-0.507542\pi\) | ||||
−0.0236928 | + | 0.999719i | \(0.507542\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 29.7698i | − | 1.38954i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 3.79232i | − | 0.176626i | −0.996093 | − | 0.0883130i | \(-0.971852\pi\) | ||
0.996093 | − | 0.0883130i | \(-0.0281476\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12.6689i | 0.588775i | 0.955686 | + | 0.294387i | \(0.0951156\pi\) | ||||
−0.955686 | + | 0.294387i | \(0.904884\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 25.8022i | − | 1.19655i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 24.6432 | 1.14035 | 0.570176 | − | 0.821523i | \(-0.306875\pi\) | ||||
0.570176 | + | 0.821523i | \(0.306875\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 26.2511 | + | 30.8533i | 1.21216 | + | 1.42467i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 18.4695i | − | 0.851030i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.27845 | −0.0587831 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.04101 | −0.139531 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −95.6647 | −4.38018 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.87711 | 0.0857674 | 0.0428837 | − | 0.999080i | \(-0.486346\pi\) | ||||
0.0428837 | + | 0.999080i | \(0.486346\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 22.0230i | 1.00416i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −5.58861 | − | 6.56839i | −0.254291 | − | 0.298872i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.66048 | −0.211622 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 14.4128i | 0.653106i | 0.945179 | + | 0.326553i | \(0.105887\pi\) | ||||
−0.945179 | + | 0.326553i | \(0.894113\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 36.5203i | − | 1.65150i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 20.6556i | 0.932175i | 0.884739 | + | 0.466087i | \(0.154337\pi\) | ||||
−0.884739 | + | 0.466087i | \(0.845663\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 10.9492i | 0.493126i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −11.2811 | −0.507049 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.984822 | + | 1.15748i | 0.0441753 | + | 0.0519200i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 36.3726i | 1.62826i | 0.580681 | + | 0.814131i | \(0.302786\pi\) | ||||
−0.580681 | + | 0.814131i | \(0.697214\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 7.31818 | 0.326952 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 9.05110 | 0.403568 | 0.201784 | − | 0.979430i | \(-0.435326\pi\) | ||||
0.201784 | + | 0.979430i | \(0.435326\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.482485 | 0.0214703 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 60.5175 | 2.68768 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 33.9980i | − | 1.50694i | −0.657484 | − | 0.753468i | \(-0.728379\pi\) | ||
0.657484 | − | 0.753468i | \(-0.271621\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 23.3970 | + | 27.4989i | 1.03502 | + | 1.21648i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −48.7043 | −2.15035 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 8.52386i | − | 0.375606i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.499103i | 0.0219505i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 43.9071i | 1.92731i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 15.5810i | − | 0.682618i | −0.939951 | − | 0.341309i | \(-0.889130\pi\) | ||
0.939951 | − | 0.341309i | \(-0.110870\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −18.6258 | −0.814449 | −0.407225 | − | 0.913328i | \(-0.633503\pi\) | ||||
−0.407225 | + | 0.913328i | \(0.633503\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 6.64057 | − | 5.65002i | 0.289818 | − | 0.246587i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 14.5535i | − | 0.633962i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.0216 | 0.957462 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −33.9672 | −1.47405 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −46.9215 | −2.03240 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 15.2510 | 0.659358 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 84.6618i | − | 3.65343i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −9.91716 | − | 1.60897i | −0.427162 | − | 0.0693033i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.29718 | −0.313730 | −0.156865 | − | 0.987620i | \(-0.550139\pi\) | ||||
−0.156865 | + | 0.987620i | \(0.550139\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 9.48465i | − | 0.407025i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 17.8125i | − | 0.763005i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 24.6305i | − | 1.05312i | −0.850137 | − | 0.526561i | \(-0.823481\pi\) | ||
0.850137 | − | 0.526561i | \(-0.176519\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 103.939i | − | 4.43601i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 17.9132 | 0.763128 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.44274 | + | 6.39695i | 0.231449 | + | 0.272026i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 12.9591i | 0.550084i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −46.8742 | −1.98612 | −0.993062 | − | 0.117595i | \(-0.962482\pi\) | ||||
−0.993062 | + | 0.117595i | \(0.962482\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.98847 | 0.210990 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8.79169 | −0.371185 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −29.9499 | −1.26224 | −0.631119 | − | 0.775686i | \(-0.717404\pi\) | ||||
−0.631119 | + | 0.775686i | \(0.717404\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 17.7201i | 0.745492i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 58.8389 | − | 50.0621i | 2.47100 | − | 2.10241i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 13.1362 | 0.550700 | 0.275350 | − | 0.961344i | \(-0.411206\pi\) | ||||
0.275350 | + | 0.961344i | \(0.411206\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.48029i | 0.229343i | 0.993403 | + | 0.114672i | \(0.0365816\pi\) | ||||
−0.993403 | + | 0.114672i | \(0.963418\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 55.8034i | 2.33122i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 0.989130i | − | 0.0412496i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8.31369i | 0.346103i | 0.984913 | + | 0.173052i | \(0.0553628\pi\) | ||||
−0.984913 | + | 0.173052i | \(0.944637\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −60.7794 | −2.52591 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 15.2962 | − | 13.0145i | 0.634594 | − | 0.539934i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 17.4687i | 0.723480i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 44.0187 | 1.81995 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −9.79972 | −0.404478 | −0.202239 | − | 0.979336i | \(-0.564822\pi\) | ||||
−0.202239 | + | 0.979336i | \(0.564822\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −23.8100 | −0.981075 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 21.8964 | 0.900697 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 11.6228i | − | 0.477290i | −0.971107 | − | 0.238645i | \(-0.923297\pi\) | ||
0.971107 | − | 0.238645i | \(-0.0767033\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.74556 | − | 3.18686i | 0.153553 | − | 0.130648i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −49.4954 | −2.02571 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 16.6809i | 0.681561i | 0.940143 | + | 0.340781i | \(0.110691\pi\) | ||||
−0.940143 | + | 0.340781i | \(0.889309\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 4.67971i | − | 0.190889i | −0.995435 | − | 0.0954446i | \(-0.969573\pi\) | ||
0.995435 | − | 0.0954446i | \(-0.0304273\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 120.346i | 4.90088i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 8.94002i | − | 0.363464i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −15.0519 | −0.610939 | −0.305469 | − | 0.952202i | \(-0.598813\pi\) | ||||
−0.305469 | + | 0.952202i | \(0.598813\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −39.1165 | + | 33.2817i | −1.58508 | + | 1.34864i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 1.94749i | − | 0.0787868i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.84689 | −0.195764 | −0.0978821 | − | 0.995198i | \(-0.531207\pi\) | ||||
−0.0978821 | + | 0.995198i | \(0.531207\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −27.6103 | −1.11335 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 21.4324 | 0.862834 | 0.431417 | − | 0.902153i | \(-0.358014\pi\) | ||||
0.431417 | + | 0.902153i | \(0.358014\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −16.4388 | −0.660731 | −0.330365 | − | 0.943853i | \(-0.607172\pi\) | ||||
−0.330365 | + | 0.943853i | \(0.607172\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 15.8417i | − | 0.635707i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 13.8569 | + | 16.2862i | 0.555164 | + | 0.652493i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 14.3835i | 0.574421i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 7.30950i | 0.291449i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 9.54286i | − | 0.379895i | −0.981794 | − | 0.189948i | \(-0.939168\pi\) | ||
0.981794 | − | 0.189948i | \(-0.0608318\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 73.9538i | 2.93940i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6.21856 | 0.246776 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 38.6965 | + | 6.27816i | 1.53321 | + | 0.248750i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4.51486i | 0.178605i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8.68996 | 0.343233 | 0.171616 | − | 0.985164i | \(-0.445101\pi\) | ||||
0.171616 | + | 0.985164i | \(0.445101\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 36.6682 | 1.44605 | 0.723026 | − | 0.690820i | \(-0.242750\pi\) | ||||
0.723026 | + | 0.690820i | \(0.242750\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.93540 | 0.115581 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 5.26708 | 0.207070 | 0.103535 | − | 0.994626i | \(-0.466985\pi\) | ||||
0.103535 | + | 0.994626i | \(0.466985\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.20253i | 0.243471i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 51.9932 | − | 44.2376i | 2.03777 | − | 1.73381i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −36.0492 | −1.41072 | −0.705358 | − | 0.708852i | \(-0.749214\pi\) | ||||
−0.705358 | + | 0.708852i | \(0.749214\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.28635i | 0.206555i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 107.262i | 4.18469i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.91466i | 0.113539i | 0.998387 | + | 0.0567695i | \(0.0180800\pi\) | ||||
−0.998387 | + | 0.0567695i | \(0.981920\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 26.9858i | 1.04963i | 0.851217 | + | 0.524814i | \(0.175865\pi\) | ||||
−0.851217 | + | 0.524814i | \(0.824135\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 34.3050 | 1.33229 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −5.21380 | − | 6.12786i | −0.202182 | − | 0.237628i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.82651i | 0.225603i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 8.48832 | 0.328177 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −18.9796 | −0.732701 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0.856509 | 0.0330160 | 0.0165080 | − | 0.999864i | \(-0.494745\pi\) | ||||
0.0165080 | + | 0.999864i | \(0.494745\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 16.0158 | 0.616449 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 25.2852i | 0.971788i | 0.874018 | + | 0.485894i | \(0.161506\pi\) | ||||
−0.874018 | + | 0.485894i | \(0.838494\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7.99036 | − | 9.39121i | −0.306642 | − | 0.360402i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −37.6053 | −1.44104 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 8.97155i | 0.343287i | 0.985159 | + | 0.171643i | \(0.0549077\pi\) | ||||
−0.985159 | + | 0.171643i | \(0.945092\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 7.48277i | − | 0.285902i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 67.1437i | − | 2.56169i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 68.1625i | − | 2.59678i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 10.2090 | 0.388368 | 0.194184 | − | 0.980965i | \(-0.437794\pi\) | ||||
0.194184 | + | 0.980965i | \(0.437794\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −19.3414 | − | 22.7323i | −0.734720 | − | 0.863528i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 13.9691i | − | 0.529877i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −15.5734 | −0.589884 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −11.4162 | −0.431802 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.01166 | 0.0382098 | 0.0191049 | − | 0.999817i | \(-0.493918\pi\) | ||||
0.0191049 | + | 0.999817i | \(0.493918\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 11.9586 | 0.451026 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − | 1.14597i | − | 0.0431597i | ||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0.827217 | + | 0.972241i | 0.0311107 | + | 0.0365649i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 28.4525 | 1.06855 | 0.534277 | − | 0.845309i | \(-0.320584\pi\) | ||||
0.534277 | + | 0.845309i | \(0.320584\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 24.9519i | 0.935770i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 7.74453i | − | 0.290035i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 8.03797i | − | 0.300603i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 53.0214i | 1.98012i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 40.3885 | 1.50624 | 0.753119 | − | 0.657884i | \(-0.228548\pi\) | ||||
0.753119 | + | 0.657884i | \(0.228548\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 17.1762 | − | 14.6141i | 0.639674 | − | 0.544257i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 17.9774i | − | 0.668586i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −5.89054 | −0.218769 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 26.6097 | 0.986900 | 0.493450 | − | 0.869774i | \(-0.335736\pi\) | ||||
0.493450 | + | 0.869774i | \(0.335736\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 71.1687 | 2.63588 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.65569 | 0.0612379 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 14.8503i | 0.548507i | 0.961657 | + | 0.274254i | \(0.0884308\pi\) | ||||
−0.961657 | + | 0.274254i | \(0.911569\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 22.7704 | + | 3.69429i | 0.839899 | + | 0.136266i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 21.9757 | 0.809485 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 18.3496i | 0.675002i | 0.941325 | + | 0.337501i | \(0.109582\pi\) | ||||
−0.941325 | + | 0.337501i | \(0.890418\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 56.1240i | − | 2.06177i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 38.1199i | 1.39848i | 0.714885 | + | 0.699242i | \(0.246479\pi\) | ||||
−0.714885 | + | 0.699242i | \(0.753521\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.118251i | 0.00433237i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 59.6644 | 2.18300 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 26.1477 | + | 30.7318i | 0.955417 | + | 1.12292i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 0.868435i | − | 0.0316896i | −0.999874 | − | 0.0158448i | \(-0.994956\pi\) | ||
0.999874 | − | 0.0158448i | \(-0.00504377\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −62.9624 | −2.29448 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 12.2429 | 0.445566 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 48.5225 | 1.76358 | 0.881791 | − | 0.471640i | \(-0.156338\pi\) | ||||
0.881791 | + | 0.471640i | \(0.156338\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −4.67842 | −0.169816 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 18.4801i | 0.669902i | 0.942236 | + | 0.334951i | \(0.108720\pi\) | ||||
−0.942236 | + | 0.334951i | \(0.891280\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 35.8935 | − | 30.5395i | 1.29943 | − | 1.10560i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 14.6099 | 0.528223 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 24.2021i | − | 0.873888i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 23.8197i | − | 0.858960i | −0.903076 | − | 0.429480i | \(-0.858697\pi\) | ||
0.903076 | − | 0.429480i | \(-0.141303\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 35.4813i | 1.27783i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 2.14017i | − | 0.0769767i | −0.999259 | − | 0.0384883i | \(-0.987746\pi\) | ||
0.999259 | − | 0.0384883i | \(-0.0122542\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7.82964 | 0.281249 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −26.1135 | + | 22.2183i | −0.936818 | + | 0.797077i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 25.4786i | 0.912864i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.824429 | 0.0295004 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −94.3419 | −3.37150 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5.60455 | 0.200035 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −20.9675 | −0.747411 | −0.373706 | − | 0.927547i | \(-0.621913\pi\) | ||||
−0.373706 | + | 0.927547i | \(0.621913\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 35.4620i | 1.26248i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −35.7074 | + | 30.3811i | −1.26961 | + | 1.08023i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 74.0581 | 2.62988 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − | 40.1092i | − | 1.42253i | ||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 46.1343i | − | 1.63416i | −0.576524 | − | 0.817080i | \(-0.695591\pi\) | ||
0.576524 | − | 0.817080i | \(-0.304409\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 0.646376i | − | 0.0228672i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 63.5260i | 2.24458i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 19.5864 | 0.691190 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.99317 | − | 1.69586i | 0.0702500 | − | 0.0597711i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 59.1775i | 2.08315i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −30.7590 | −1.08143 | −0.540715 | − | 0.841206i | \(-0.681846\pi\) | ||||
−0.540715 | + | 0.841206i | \(0.681846\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −26.1227 | −0.917293 | −0.458647 | − | 0.888619i | \(-0.651666\pi\) | ||||
−0.458647 | + | 0.888619i | \(0.651666\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 54.5847 | 1.91437 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 11.0820 | 0.388187 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 2.70876i | − | 0.0947675i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 75.4697 | + | 88.7008i | 2.63713 | + | 3.09946i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −51.8580 | −1.80986 | −0.904928 | − | 0.425565i | \(-0.860075\pi\) | ||||
−0.904928 | + | 0.425565i | \(0.860075\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 32.0866i | − | 1.11847i | −0.829010 | − | 0.559234i | \(-0.811095\pi\) | ||
0.829010 | − | 0.559234i | \(-0.188905\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 4.72983i | − | 0.164672i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 19.1319i | − | 0.665282i | −0.943054 | − | 0.332641i | \(-0.892060\pi\) | ||
0.943054 | − | 0.332641i | \(-0.107940\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 14.1288i | − | 0.490714i | −0.969433 | − | 0.245357i | \(-0.921095\pi\) | ||
0.969433 | − | 0.245357i | \(-0.0789052\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 24.2926 | 0.842701 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 12.8435 | + | 2.08374i | 0.445000 | + | 0.0721973i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.22069i | 0.0768503i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 125.398 | 4.33439 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −41.3350 | −1.42704 | −0.713522 | − | 0.700633i | \(-0.752901\pi\) | ||||
−0.713522 | + | 0.700633i | \(0.752901\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.69845 | 0.196498 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 30.0554 | 1.03516 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 18.3640i | 0.631740i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 18.0148 | − | 15.3276i | 0.618996 | − | 0.526663i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −90.4862 | −3.10548 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.88968i | 0.133337i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 18.9283i | 0.648092i | 0.946041 | + | 0.324046i | \(0.105043\pi\) | ||||
−0.946041 | + | 0.324046i | \(0.894957\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 23.9023i | − | 0.817442i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 24.1669i | − | 0.825527i | −0.910838 | − | 0.412763i | \(-0.864564\pi\) | ||
0.910838 | − | 0.412763i | \(-0.135436\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −32.7102 | −1.11606 | −0.558028 | − | 0.829822i | \(-0.688442\pi\) | ||||
−0.558028 | + | 0.829822i | \(0.688442\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −47.3377 | − | 55.6367i | −1.61326 | − | 1.89609i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 41.8221i | − | 1.42364i | −0.702361 | − | 0.711821i | \(-0.747871\pi\) | ||
0.702361 | − | 0.711821i | \(-0.252129\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −13.3236 | −0.453014 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −44.6367 | −1.51594 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.55631 | 0.154562 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −85.7486 | −2.90548 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 36.6313i | − | 1.23978i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.71449 | + | 2.01507i | 0.0579604 | + | 0.0681219i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 18.4511 | 0.623050 | 0.311525 | − | 0.950238i | \(-0.399160\pi\) | ||||
0.311525 | + | 0.950238i | \(0.399160\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 74.1919i | 2.50243i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 41.0743i | 1.38383i | 0.721979 | + | 0.691915i | \(0.243233\pi\) | ||||
−0.721979 | + | 0.691915i | \(0.756767\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 30.8276i | − | 1.03743i | −0.854946 | − | 0.518716i | \(-0.826410\pi\) | ||
0.854946 | − | 0.518716i | \(-0.173590\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − | 14.2414i | − | 0.478719i | ||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 39.7932 | 1.33612 | 0.668062 | − | 0.744105i | \(-0.267124\pi\) | ||||
0.668062 | + | 0.744105i | \(0.267124\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 10.6617 | + | 12.5308i | 0.357581 | + | 0.420271i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 41.9088i | − | 1.40400i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.05749 | −0.0353876 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 25.6905 | 0.858739 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 18.2551 | 0.609519 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −46.1208 | −1.53821 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 22.6233i | − | 0.753693i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 5.03272 | + | 5.91504i | 0.167478 | + | 0.196840i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.87811 | 0.0956715 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 21.9225i | − | 0.727925i | −0.931414 | − | 0.363962i | \(-0.881424\pi\) | ||
0.931414 | − | 0.363962i | \(-0.118576\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.79232i | 0.125783i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 16.2898i | 0.539704i | 0.962902 | + | 0.269852i | \(0.0869749\pi\) | ||||
−0.962902 | + | 0.269852i | \(0.913025\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 10.8949i | − | 0.360570i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 43.5784 | 1.44066 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −10.6524 | + | 9.06340i | −0.351772 | + | 0.299300i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 36.2223i | − | 1.19486i | −0.801920 | − | 0.597432i | \(-0.796188\pi\) | ||
0.801920 | − | 0.597432i | \(-0.203812\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 37.4552 | 1.23419 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −3.21690 | −0.105886 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.93243 | −0.129297 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 66.9974 | 2.20048 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 14.6208i | 0.479692i | 0.970811 | + | 0.239846i | \(0.0770970\pi\) | ||||
−0.970811 | + | 0.239846i | \(0.922903\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.40907 | − | 21.0123i | 0.111728 | − | 0.688652i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −47.9635 | −1.57026 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 2.66783i | − | 0.0872473i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 5.49926i | − | 0.179653i | −0.995957 | − | 0.0898265i | \(-0.971369\pi\) | ||
0.995957 | − | 0.0898265i | \(-0.0286312\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 25.5535i | 0.833908i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 13.1893i | − | 0.429959i | −0.976619 | − | 0.214979i | \(-0.931032\pi\) | ||
0.976619 | − | 0.214979i | \(-0.0689684\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −8.28724 | −0.269870 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 27.4590 | + | 32.2730i | 0.893242 | + | 1.04984i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 3.02749i | − | 0.0983803i | −0.998789 | − | 0.0491901i | \(-0.984336\pi\) | ||
0.998789 | − | 0.0491901i | \(-0.0156640\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −76.4258 | −2.48089 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −30.6954 | −0.995366 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.56005 | −0.115321 | −0.0576607 | − | 0.998336i | \(-0.518364\pi\) | ||||
−0.0576607 | + | 0.998336i | \(0.518364\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −16.9335 | −0.547954 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 27.8613i | 0.900626i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 15.0783 | − | 12.8292i | 0.486905 | − | 0.414275i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 30.3032 | 0.977523 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 119.873i | 3.86284i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 18.4434i | − | 0.593715i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 36.3856i | 1.17008i | 0.811004 | + | 0.585040i | \(0.198921\pi\) | ||||
−0.811004 | + | 0.585040i | \(0.801079\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 18.6277i | − | 0.598408i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −41.0067 | −1.31597 | −0.657984 | − | 0.753032i | \(-0.728590\pi\) | ||||
−0.657984 | + | 0.753032i | \(0.728590\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 28.1487 | − | 23.9499i | 0.902406 | − | 0.767798i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 18.4557i | 0.591055i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −48.3681 | −1.54743 | −0.773716 | − | 0.633533i | \(-0.781604\pi\) | ||||
−0.773716 | + | 0.633533i | \(0.781604\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 11.6001 | 0.370740 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 140.006 | 4.47005 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 3.47969 | 0.110985 | 0.0554924 | − | 0.998459i | \(-0.482327\pi\) | ||||
0.0554924 | + | 0.998459i | \(0.482327\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6.64444i | 0.211709i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.30921 | − | 1.96476i | 0.0735030 | − | 0.0625389i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.881061 | 0.0280161 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 38.6592i | 1.22805i | 0.789286 | + | 0.614025i | \(0.210451\pi\) | ||||
−0.789286 | + | 0.614025i | \(0.789549\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 75.7554i | − | 2.40403i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 15.0193i | − | 0.476144i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 4.22709i | − | 0.133873i | −0.997757 | − | 0.0669366i | \(-0.978677\pi\) | ||
0.997757 | − | 0.0669366i | \(-0.0213225\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −62.9811 | −1.99263 |
(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 | 2240.2.k.g.1791.1 | 16 | ||
4.3 | odd | 2 | 2240.2.k.f.1791.15 | 16 | |||
7.6 | odd | 2 | 2240.2.k.f.1791.16 | 16 | |||
8.3 | odd | 2 | 1120.2.k.a.671.2 | yes | 16 | ||
8.5 | even | 2 | 1120.2.k.b.671.16 | yes | 16 | ||
28.27 | even | 2 | inner | 2240.2.k.g.1791.2 | 16 | ||
56.13 | odd | 2 | 1120.2.k.a.671.1 | ✓ | 16 | ||
56.27 | even | 2 | 1120.2.k.b.671.15 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1120.2.k.a.671.1 | ✓ | 16 | 56.13 | odd | 2 | ||
1120.2.k.a.671.2 | yes | 16 | 8.3 | odd | 2 | ||
1120.2.k.b.671.15 | yes | 16 | 56.27 | even | 2 | ||
1120.2.k.b.671.16 | yes | 16 | 8.5 | even | 2 | ||
2240.2.k.f.1791.15 | 16 | 4.3 | odd | 2 | |||
2240.2.k.f.1791.16 | 16 | 7.6 | odd | 2 | |||
2240.2.k.g.1791.1 | 16 | 1.1 | even | 1 | trivial | ||
2240.2.k.g.1791.2 | 16 | 28.27 | even | 2 | inner |