Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1805,2,Mod(1084,1805)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1805, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1805.1084");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1805 = 5 \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1805.b (of order \(2\), degree \(1\), 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: | \(14.4129975648\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.4227136.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 6x^{4} + 7x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 95) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1084.2 | ||
Root | \(-1.15904i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1805.1084 |
Dual form | 1805.2.b.f.1084.5 |
$q$-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 \(\left(\mathbb{Z}/1805\mathbb{Z}\right)^\times\).
\(n\) | \(362\) | \(1446\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 0.862781i | − | 0.610078i | −0.952340 | − | 0.305039i | \(-0.901330\pi\) | ||
0.952340 | − | 0.305039i | \(-0.0986696\pi\) | |||||||
\(3\) | 3.07914i | 1.77774i | 0.458159 | + | 0.888870i | \(0.348509\pi\) | ||||
−0.458159 | + | 0.888870i | \(0.651491\pi\) | |||||||
\(4\) | 1.25561 | 0.627804 | ||||||||
\(5\) | −1.91223 | − | 1.15904i | −0.855175 | − | 0.518340i | ||||
\(6\) | 2.65662 | 1.08456 | ||||||||
\(7\) | − | 0.566520i | − | 0.214124i | −0.994252 | − | 0.107062i | \(-0.965856\pi\) | ||
0.994252 | − | 0.107062i | \(-0.0341444\pi\) | |||||||
\(8\) | − | 2.80888i | − | 0.993088i | ||||||
\(9\) | −6.48108 | −2.16036 | ||||||||
\(10\) | −1.00000 | + | 1.64984i | −0.316228 | + | 0.521724i | ||||
\(11\) | −1.91223 | −0.576559 | −0.288279 | − | 0.957546i | \(-0.593083\pi\) | ||||
−0.288279 | + | 0.957546i | \(0.593083\pi\) | |||||||
\(12\) | 3.86619i | 1.11607i | ||||||||
\(13\) | 0.194531i | 0.0539533i | 0.999636 | + | 0.0269766i | \(0.00858797\pi\) | ||||
−0.999636 | + | 0.0269766i | \(0.991412\pi\) | |||||||
\(14\) | −0.488783 | −0.130633 | ||||||||
\(15\) | 3.56885 | − | 5.88801i | 0.921473 | − | 1.52028i | ||||
\(16\) | 0.0877708 | 0.0219427 | ||||||||
\(17\) | − | 5.29549i | − | 1.28435i | −0.766560 | − | 0.642173i | \(-0.778033\pi\) | ||
0.766560 | − | 0.642173i | \(-0.221967\pi\) | |||||||
\(18\) | 5.59175i | 1.31799i | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | −2.40101 | − | 1.45530i | −0.536883 | − | 0.325416i | ||||
\(21\) | 1.74439 | 0.380657 | ||||||||
\(22\) | 1.64984i | 0.351746i | ||||||||
\(23\) | 3.37540i | 0.703819i | 0.936034 | + | 0.351910i | \(0.114468\pi\) | ||||
−0.936034 | + | 0.351910i | \(0.885532\pi\) | |||||||
\(24\) | 8.64892 | 1.76545 | ||||||||
\(25\) | 2.31324 | + | 4.43271i | 0.462648 | + | 0.886542i | ||||
\(26\) | 0.167838 | 0.0329157 | ||||||||
\(27\) | − | 10.7187i | − | 2.06282i | ||||||
\(28\) | − | 0.711327i | − | 0.134428i | ||||||
\(29\) | 8.73669 | 1.62236 | 0.811181 | − | 0.584795i | \(-0.198825\pi\) | ||||
0.811181 | + | 0.584795i | \(0.198825\pi\) | |||||||
\(30\) | −5.08007 | − | 3.07914i | −0.927489 | − | 0.562171i | ||||
\(31\) | 5.65662 | 1.01596 | 0.507980 | − | 0.861369i | \(-0.330393\pi\) | ||||
0.507980 | + | 0.861369i | \(0.330393\pi\) | |||||||
\(32\) | − | 5.69348i | − | 1.00648i | ||||||
\(33\) | − | 5.88801i | − | 1.02497i | ||||||
\(34\) | −4.56885 | −0.783551 | ||||||||
\(35\) | −0.656620 | + | 1.08332i | −0.110989 | + | 0.183114i | ||||
\(36\) | −8.13770 | −1.35628 | ||||||||
\(37\) | − | 0.955582i | − | 0.157097i | −0.996910 | − | 0.0785484i | \(-0.974971\pi\) | ||
0.996910 | − | 0.0785484i | \(-0.0250285\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.598988 | −0.0959149 | ||||||||
\(40\) | −3.25561 | + | 5.37122i | −0.514757 | + | 0.849264i | ||||
\(41\) | 10.0499 | 1.56954 | 0.784768 | − | 0.619790i | \(-0.212782\pi\) | ||||
0.784768 | + | 0.619790i | \(0.212782\pi\) | |||||||
\(42\) | − | 1.50503i | − | 0.232231i | ||||||
\(43\) | − | 4.93243i | − | 0.752189i | −0.926581 | − | 0.376094i | \(-0.877267\pi\) | ||
0.926581 | − | 0.376094i | \(-0.122733\pi\) | |||||||
\(44\) | −2.40101 | −0.361966 | ||||||||
\(45\) | 12.3933 | + | 7.51185i | 1.84749 | + | 1.11980i | ||||
\(46\) | 2.91223 | 0.429385 | ||||||||
\(47\) | − | 8.83942i | − | 1.28936i | −0.764452 | − | 0.644681i | \(-0.776990\pi\) | ||
0.764452 | − | 0.644681i | \(-0.223010\pi\) | |||||||
\(48\) | 0.270258i | 0.0390084i | ||||||||
\(49\) | 6.67906 | 0.954151 | ||||||||
\(50\) | 3.82446 | − | 1.99582i | 0.540860 | − | 0.282252i | ||||
\(51\) | 16.3055 | 2.28323 | ||||||||
\(52\) | 0.244255i | 0.0338721i | ||||||||
\(53\) | − | 8.20610i | − | 1.12719i | −0.826050 | − | 0.563597i | \(-0.809417\pi\) | ||
0.826050 | − | 0.563597i | \(-0.190583\pi\) | |||||||
\(54\) | −9.24791 | −1.25848 | ||||||||
\(55\) | 3.65662 | + | 2.21635i | 0.493059 | + | 0.298853i | ||||
\(56\) | −1.59128 | −0.212644 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | − | 7.53785i | − | 0.989768i | ||||||
\(59\) | −3.71425 | −0.483554 | −0.241777 | − | 0.970332i | \(-0.577730\pi\) | ||||
−0.241777 | + | 0.970332i | \(0.577730\pi\) | |||||||
\(60\) | 4.48108 | − | 7.39304i | 0.578505 | − | 0.954438i | ||||
\(61\) | −3.51122 | −0.449565 | −0.224783 | − | 0.974409i | \(-0.572167\pi\) | ||||
−0.224783 | + | 0.974409i | \(0.572167\pi\) | |||||||
\(62\) | − | 4.88043i | − | 0.619815i | ||||||
\(63\) | 3.67166i | 0.462586i | ||||||||
\(64\) | −4.73669 | −0.592086 | ||||||||
\(65\) | 0.225470 | − | 0.371988i | 0.0279661 | − | 0.0461395i | ||||
\(66\) | −5.08007 | −0.625313 | ||||||||
\(67\) | − | 4.04365i | − | 0.494010i | −0.969014 | − | 0.247005i | \(-0.920554\pi\) | ||
0.969014 | − | 0.247005i | \(-0.0794464\pi\) | |||||||
\(68\) | − | 6.64906i | − | 0.806318i | ||||||
\(69\) | −10.3933 | −1.25121 | ||||||||
\(70\) | 0.934664 | + | 0.566520i | 0.111714 | + | 0.0677121i | ||||
\(71\) | 5.19533 | 0.616572 | 0.308286 | − | 0.951294i | \(-0.400245\pi\) | ||||
0.308286 | + | 0.951294i | \(0.400245\pi\) | |||||||
\(72\) | 18.2046i | 2.14543i | ||||||||
\(73\) | 8.60409i | 1.00703i | 0.863986 | + | 0.503516i | \(0.167961\pi\) | ||||
−0.863986 | + | 0.503516i | \(0.832039\pi\) | |||||||
\(74\) | −0.824458 | −0.0958413 | ||||||||
\(75\) | −13.6489 | + | 7.12278i | −1.57604 | + | 0.822468i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.08332i | 0.123455i | ||||||||
\(78\) | 0.516796i | 0.0585156i | ||||||||
\(79\) | −6.62648 | −0.745537 | −0.372769 | − | 0.927924i | \(-0.621592\pi\) | ||||
−0.372769 | + | 0.927924i | \(0.621592\pi\) | |||||||
\(80\) | −0.167838 | − | 0.101730i | −0.0187649 | − | 0.0113738i | ||||
\(81\) | 13.5611 | 1.50679 | ||||||||
\(82\) | − | 8.67089i | − | 0.957539i | ||||||
\(83\) | − | 4.51737i | − | 0.495845i | −0.968780 | − | 0.247923i | \(-0.920252\pi\) | ||
0.968780 | − | 0.247923i | \(-0.0797479\pi\) | |||||||
\(84\) | 2.19027 | 0.238978 | ||||||||
\(85\) | −6.13770 | + | 10.1262i | −0.665727 | + | 1.09834i | ||||
\(86\) | −4.25561 | −0.458894 | ||||||||
\(87\) | 26.9014i | 2.88414i | ||||||||
\(88\) | 5.37122i | 0.572574i | ||||||||
\(89\) | −3.37352 | −0.357592 | −0.178796 | − | 0.983886i | \(-0.557220\pi\) | ||||
−0.178796 | + | 0.983886i | \(0.557220\pi\) | |||||||
\(90\) | 6.48108 | − | 10.6927i | 0.683166 | − | 1.12711i | ||||
\(91\) | 0.110206 | 0.0115527 | ||||||||
\(92\) | 4.23818i | 0.441861i | ||||||||
\(93\) | 17.4175i | 1.80611i | ||||||||
\(94\) | −7.62648 | −0.786612 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 17.5310 | 1.78925 | ||||||||
\(97\) | − | 15.1922i | − | 1.54254i | −0.636510 | − | 0.771268i | \(-0.719623\pi\) | ||
0.636510 | − | 0.771268i | \(-0.280377\pi\) | |||||||
\(98\) | − | 5.76256i | − | 0.582107i | ||||||
\(99\) | 12.3933 | 1.24557 | ||||||||
\(100\) | 2.90453 | + | 5.56575i | 0.290453 | + | 0.556575i | ||||
\(101\) | 3.54136 | 0.352378 | 0.176189 | − | 0.984356i | \(-0.443623\pi\) | ||||
0.176189 | + | 0.984356i | \(0.443623\pi\) | |||||||
\(102\) | − | 14.0681i | − | 1.39295i | ||||||
\(103\) | 15.6919i | 1.54617i | 0.634301 | + | 0.773086i | \(0.281288\pi\) | ||||
−0.634301 | + | 0.773086i | \(0.718712\pi\) | |||||||
\(104\) | 0.546415 | 0.0535804 | ||||||||
\(105\) | −3.33568 | − | 2.02182i | −0.325529 | − | 0.197310i | ||||
\(106\) | −7.08007 | −0.687677 | ||||||||
\(107\) | − | 1.05731i | − | 0.102214i | −0.998693 | − | 0.0511071i | \(-0.983725\pi\) | ||
0.998693 | − | 0.0511071i | \(-0.0162750\pi\) | |||||||
\(108\) | − | 13.4585i | − | 1.29505i | ||||||
\(109\) | 6.74439 | 0.645996 | 0.322998 | − | 0.946400i | \(-0.395309\pi\) | ||||
0.322998 | + | 0.946400i | \(0.395309\pi\) | |||||||
\(110\) | 1.91223 | − | 3.15486i | 0.182324 | − | 0.300804i | ||||
\(111\) | 2.94237 | 0.279277 | ||||||||
\(112\) | − | 0.0497239i | − | 0.00469847i | ||||||
\(113\) | − | 7.90091i | − | 0.743255i | −0.928382 | − | 0.371627i | \(-0.878800\pi\) | ||
0.928382 | − | 0.371627i | \(-0.121200\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.91223 | − | 6.45453i | 0.364817 | − | 0.601888i | ||||
\(116\) | 10.9699 | 1.01853 | ||||||||
\(117\) | − | 1.26077i | − | 0.116558i | ||||||
\(118\) | 3.20459i | 0.295006i | ||||||||
\(119\) | −3.00000 | −0.275010 | ||||||||
\(120\) | −16.5387 | − | 10.0245i | −1.50977 | − | 0.915104i | ||||
\(121\) | −7.34338 | −0.667580 | ||||||||
\(122\) | 3.02941i | 0.274270i | ||||||||
\(123\) | 30.9451i | 2.79023i | ||||||||
\(124\) | 7.10250 | 0.637824 | ||||||||
\(125\) | 0.714253 | − | 11.1575i | 0.0638847 | − | 0.997957i | ||||
\(126\) | 3.16784 | 0.282213 | ||||||||
\(127\) | 8.47636i | 0.752155i | 0.926588 | + | 0.376078i | \(0.122727\pi\) | ||||
−0.926588 | + | 0.376078i | \(0.877273\pi\) | |||||||
\(128\) | − | 7.30024i | − | 0.645256i | ||||||
\(129\) | 15.1876 | 1.33720 | ||||||||
\(130\) | −0.320945 | − | 0.194531i | −0.0281487 | − | 0.0170615i | ||||
\(131\) | 1.87439 | 0.163766 | 0.0818830 | − | 0.996642i | \(-0.473907\pi\) | ||||
0.0818830 | + | 0.996642i | \(0.473907\pi\) | |||||||
\(132\) | − | 7.39304i | − | 0.643482i | ||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −3.48878 | −0.301385 | ||||||||
\(135\) | −12.4234 | + | 20.4966i | −1.06924 | + | 1.76407i | ||||
\(136\) | −14.8744 | −1.27547 | ||||||||
\(137\) | − | 12.4614i | − | 1.06465i | −0.846542 | − | 0.532323i | \(-0.821319\pi\) | ||
0.846542 | − | 0.532323i | \(-0.178681\pi\) | |||||||
\(138\) | 8.96715i | 0.763334i | ||||||||
\(139\) | 0.313241 | 0.0265687 | 0.0132844 | − | 0.999912i | \(-0.495771\pi\) | ||||
0.0132844 | + | 0.999912i | \(0.495771\pi\) | |||||||
\(140\) | −0.824458 | + | 1.36022i | −0.0696794 | + | 0.114960i | ||||
\(141\) | 27.2178 | 2.29215 | ||||||||
\(142\) | − | 4.48243i | − | 0.376157i | ||||||
\(143\) | − | 0.371988i | − | 0.0311072i | ||||||
\(144\) | −0.568850 | −0.0474041 | ||||||||
\(145\) | −16.7065 | − | 10.1262i | −1.38740 | − | 0.840935i | ||||
\(146\) | 7.42345 | 0.614369 | ||||||||
\(147\) | 20.5657i | 1.69623i | ||||||||
\(148\) | − | 1.19984i | − | 0.0986260i | ||||||
\(149\) | −4.36581 | −0.357661 | −0.178831 | − | 0.983880i | \(-0.557231\pi\) | ||||
−0.178831 | + | 0.983880i | \(0.557231\pi\) | |||||||
\(150\) | 6.14540 | + | 11.7760i | 0.501770 | + | 0.961509i | ||||
\(151\) | 0.197977 | 0.0161111 | 0.00805555 | − | 0.999968i | \(-0.497436\pi\) | ||||
0.00805555 | + | 0.999968i | \(0.497436\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 34.3205i | 2.77465i | ||||||||
\(154\) | 0.934664 | 0.0753174 | ||||||||
\(155\) | −10.8168 | − | 6.55626i | −0.868823 | − | 0.526612i | ||||
\(156\) | −0.752095 | −0.0602158 | ||||||||
\(157\) | − | 15.7700i | − | 1.25858i | −0.777171 | − | 0.629290i | \(-0.783346\pi\) | ||
0.777171 | − | 0.629290i | \(-0.216654\pi\) | |||||||
\(158\) | 5.71720i | 0.454836i | ||||||||
\(159\) | 25.2677 | 2.00386 | ||||||||
\(160\) | −6.59899 | + | 10.8872i | −0.521696 | + | 0.860712i | ||||
\(161\) | 1.91223 | 0.150705 | ||||||||
\(162\) | − | 11.7003i | − | 0.919262i | ||||||
\(163\) | 9.18768i | 0.719635i | 0.933023 | + | 0.359817i | \(0.117161\pi\) | ||||
−0.933023 | + | 0.359817i | \(0.882839\pi\) | |||||||
\(164\) | 12.6188 | 0.985361 | ||||||||
\(165\) | −6.82446 | + | 11.2592i | −0.531283 | + | 0.876530i | ||||
\(166\) | −3.89750 | −0.302505 | ||||||||
\(167\) | 3.07021i | 0.237580i | 0.992919 | + | 0.118790i | \(0.0379015\pi\) | ||||
−0.992919 | + | 0.118790i | \(0.962099\pi\) | |||||||
\(168\) | − | 4.89978i | − | 0.378026i | ||||||
\(169\) | 12.9622 | 0.997089 | ||||||||
\(170\) | 8.73669 | + | 5.29549i | 0.670073 | + | 0.406146i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − | 6.19320i | − | 0.472227i | ||||||
\(173\) | 10.4135i | 0.791726i | 0.918310 | + | 0.395863i | \(0.129554\pi\) | ||||
−0.918310 | + | 0.395863i | \(0.870446\pi\) | |||||||
\(174\) | 23.2101 | 1.75955 | ||||||||
\(175\) | 2.51122 | − | 1.31050i | 0.189830 | − | 0.0990642i | ||||
\(176\) | −0.167838 | −0.0126513 | ||||||||
\(177\) | − | 11.4367i | − | 0.859634i | ||||||
\(178\) | 2.91061i | 0.218159i | ||||||||
\(179\) | 13.4432 | 1.00479 | 0.502397 | − | 0.864637i | \(-0.332451\pi\) | ||||
0.502397 | + | 0.864637i | \(0.332451\pi\) | |||||||
\(180\) | 15.5611 | + | 9.43194i | 1.15986 | + | 0.703015i | ||||
\(181\) | 7.96216 | 0.591823 | 0.295911 | − | 0.955215i | \(-0.404377\pi\) | ||||
0.295911 | + | 0.955215i | \(0.404377\pi\) | |||||||
\(182\) | − | 0.0950835i | − | 0.00704806i | ||||||
\(183\) | − | 10.8115i | − | 0.799210i | ||||||
\(184\) | 9.48108 | 0.698954 | ||||||||
\(185\) | −1.10756 | + | 1.82729i | −0.0814295 | + | 0.134345i | ||||
\(186\) | 15.0275 | 1.10187 | ||||||||
\(187\) | 10.1262i | 0.740501i | ||||||||
\(188\) | − | 11.0988i | − | 0.809467i | ||||||
\(189\) | −6.07236 | −0.441699 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −14.0999 | −1.02023 | −0.510115 | − | 0.860106i | \(-0.670397\pi\) | ||||
−0.510115 | + | 0.860106i | \(0.670397\pi\) | |||||||
\(192\) | − | 14.5849i | − | 1.05257i | ||||||
\(193\) | 3.97685i | 0.286260i | 0.989704 | + | 0.143130i | \(0.0457167\pi\) | ||||
−0.989704 | + | 0.143130i | \(0.954283\pi\) | |||||||
\(194\) | −13.1076 | −0.941068 | ||||||||
\(195\) | 1.14540 | + | 0.694253i | 0.0820240 | + | 0.0497165i | ||||
\(196\) | 8.38628 | 0.599020 | ||||||||
\(197\) | − | 18.3494i | − | 1.30734i | −0.756781 | − | 0.653669i | \(-0.773229\pi\) | ||
0.756781 | − | 0.653669i | \(-0.226771\pi\) | |||||||
\(198\) | − | 10.6927i | − | 0.759898i | ||||||
\(199\) | 1.60669 | 0.113895 | 0.0569477 | − | 0.998377i | \(-0.481863\pi\) | ||||
0.0569477 | + | 0.998377i | \(0.481863\pi\) | |||||||
\(200\) | 12.4509 | − | 6.49761i | 0.880414 | − | 0.459450i | ||||
\(201\) | 12.4509 | 0.878222 | ||||||||
\(202\) | − | 3.05542i | − | 0.214978i | ||||||
\(203\) | − | 4.94951i | − | 0.347387i | ||||||
\(204\) | 20.4734 | 1.43342 | ||||||||
\(205\) | −19.2178 | − | 11.6483i | −1.34223 | − | 0.813552i | ||||
\(206\) | 13.5387 | 0.943287 | ||||||||
\(207\) | − | 21.8762i | − | 1.52050i | ||||||
\(208\) | 0.0170742i | 0.00118388i | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −1.74439 | + | 2.87796i | −0.120374 | + | 0.198598i | ||||
\(211\) | −6.09986 | −0.419931 | −0.209966 | − | 0.977709i | \(-0.567335\pi\) | ||||
−0.209966 | + | 0.977709i | \(0.567335\pi\) | |||||||
\(212\) | − | 10.3036i | − | 0.707658i | ||||||
\(213\) | 15.9971i | 1.09611i | ||||||||
\(214\) | −0.912229 | −0.0623587 | ||||||||
\(215\) | −5.71690 | + | 9.43194i | −0.389889 | + | 0.643253i | ||||
\(216\) | −30.1076 | −2.04856 | ||||||||
\(217\) | − | 3.20459i | − | 0.217542i | ||||||
\(218\) | − | 5.81893i | − | 0.394108i | ||||||
\(219\) | −26.4932 | −1.79024 | ||||||||
\(220\) | 4.59128 | + | 2.78287i | 0.309544 | + | 0.187621i | ||||
\(221\) | 1.03014 | 0.0692946 | ||||||||
\(222\) | − | 2.53862i | − | 0.170381i | ||||||
\(223\) | 17.2253i | 1.15349i | 0.816925 | + | 0.576744i | \(0.195677\pi\) | ||||
−0.816925 | + | 0.576744i | \(0.804323\pi\) | |||||||
\(224\) | −3.22547 | −0.215511 | ||||||||
\(225\) | −14.9923 | − | 28.7287i | −0.999486 | − | 1.91525i | ||||
\(226\) | −6.81675 | −0.453444 | ||||||||
\(227\) | − | 1.18505i | − | 0.0786542i | −0.999226 | − | 0.0393271i | \(-0.987479\pi\) | ||
0.999226 | − | 0.0393271i | \(-0.0125214\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.24791 | −0.412873 | −0.206437 | − | 0.978460i | \(-0.566187\pi\) | ||||
−0.206437 | + | 0.978460i | \(0.566187\pi\) | |||||||
\(230\) | −5.56885 | − | 3.37540i | −0.367199 | − | 0.222567i | ||||
\(231\) | −3.33568 | −0.219471 | ||||||||
\(232\) | − | 24.5403i | − | 1.61115i | ||||||
\(233\) | − | 2.75687i | − | 0.180609i | −0.995914 | − | 0.0903043i | \(-0.971216\pi\) | ||
0.995914 | − | 0.0903043i | \(-0.0287840\pi\) | |||||||
\(234\) | −1.08777 | −0.0711098 | ||||||||
\(235\) | −10.2453 | + | 16.9030i | −0.668327 | + | 1.10263i | ||||
\(236\) | −4.66365 | −0.303578 | ||||||||
\(237\) | − | 20.4038i | − | 1.32537i | ||||||
\(238\) | 2.58834i | 0.167777i | ||||||||
\(239\) | −17.3055 | −1.11940 | −0.559701 | − | 0.828695i | \(-0.689084\pi\) | ||||
−0.559701 | + | 0.828695i | \(0.689084\pi\) | |||||||
\(240\) | 0.313241 | − | 0.516796i | 0.0202196 | − | 0.0333590i | ||||
\(241\) | −4.78662 | −0.308333 | −0.154167 | − | 0.988045i | \(-0.549269\pi\) | ||||
−0.154167 | + | 0.988045i | \(0.549269\pi\) | |||||||
\(242\) | 6.33573i | 0.407276i | ||||||||
\(243\) | 9.60047i | 0.615870i | ||||||||
\(244\) | −4.40872 | −0.282239 | ||||||||
\(245\) | −12.7719 | − | 7.74131i | −0.815966 | − | 0.494574i | ||||
\(246\) | 26.6988 | 1.70226 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | − | 15.8888i | − | 1.00894i | ||||||
\(249\) | 13.9096 | 0.881484 | ||||||||
\(250\) | −9.62648 | − | 0.616244i | −0.608832 | − | 0.0389747i | ||||
\(251\) | −26.2479 | −1.65675 | −0.828377 | − | 0.560172i | \(-0.810735\pi\) | ||||
−0.828377 | + | 0.560172i | \(0.810735\pi\) | |||||||
\(252\) | 4.61017i | 0.290413i | ||||||||
\(253\) | − | 6.45453i | − | 0.405793i | ||||||
\(254\) | 7.31324 | 0.458874 | ||||||||
\(255\) | −31.1799 | − | 18.8988i | −1.95256 | − | 1.18349i | ||||
\(256\) | −15.7719 | −0.985743 | ||||||||
\(257\) | 22.2505i | 1.38795i | 0.720000 | + | 0.693974i | \(0.244142\pi\) | ||||
−0.720000 | + | 0.693974i | \(0.755858\pi\) | |||||||
\(258\) | − | 13.1036i | − | 0.815794i | ||||||
\(259\) | −0.541356 | −0.0336382 | ||||||||
\(260\) | 0.283102 | − | 0.467072i | 0.0175573 | − | 0.0289666i | ||||
\(261\) | −56.6232 | −3.50489 | ||||||||
\(262\) | − | 1.61719i | − | 0.0999101i | ||||||
\(263\) | 8.81341i | 0.543458i | 0.962374 | + | 0.271729i | \(0.0875955\pi\) | ||||
−0.962374 | + | 0.271729i | \(0.912405\pi\) | |||||||
\(264\) | −16.5387 | −1.01789 | ||||||||
\(265\) | −9.51122 | + | 15.6919i | −0.584269 | + | 0.963948i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 10.3875i | − | 0.635706i | ||||||
\(268\) | − | 5.07724i | − | 0.310142i | ||||||
\(269\) | 4.76418 | 0.290477 | 0.145239 | − | 0.989397i | \(-0.453605\pi\) | ||||
0.145239 | + | 0.989397i | \(0.453605\pi\) | |||||||
\(270\) | 17.6841 | + | 10.7187i | 1.07622 | + | 0.652320i | ||||
\(271\) | 3.51892 | 0.213759 | 0.106880 | − | 0.994272i | \(-0.465914\pi\) | ||||
0.106880 | + | 0.994272i | \(0.465914\pi\) | |||||||
\(272\) | − | 0.464790i | − | 0.0281820i | ||||||
\(273\) | 0.339339i | 0.0205377i | ||||||||
\(274\) | −10.7514 | −0.649517 | ||||||||
\(275\) | −4.42345 | − | 8.47636i | −0.266744 | − | 0.511144i | ||||
\(276\) | −13.0499 | −0.785513 | ||||||||
\(277\) | − | 32.7724i | − | 1.96910i | −0.175098 | − | 0.984551i | \(-0.556024\pi\) | ||
0.175098 | − | 0.984551i | \(-0.443976\pi\) | |||||||
\(278\) | − | 0.270258i | − | 0.0162090i | ||||||
\(279\) | −36.6610 | −2.19484 | ||||||||
\(280\) | 3.04290 | + | 1.84437i | 0.181848 | + | 0.110222i | ||||
\(281\) | 9.91993 | 0.591774 | 0.295887 | − | 0.955223i | \(-0.404385\pi\) | ||||
0.295887 | + | 0.955223i | \(0.404385\pi\) | |||||||
\(282\) | − | 23.4830i | − | 1.39839i | ||||||
\(283\) | − | 2.47182i | − | 0.146935i | −0.997298 | − | 0.0734673i | \(-0.976594\pi\) | ||
0.997298 | − | 0.0734673i | \(-0.0234064\pi\) | |||||||
\(284\) | 6.52330 | 0.387087 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.320945 | −0.0189779 | ||||||||
\(287\) | − | 5.69348i | − | 0.336076i | ||||||
\(288\) | 36.8999i | 2.17435i | ||||||||
\(289\) | −11.0422 | −0.649543 | ||||||||
\(290\) | −8.73669 | + | 14.4141i | −0.513036 | + | 0.846425i | ||||
\(291\) | 46.7789 | 2.74223 | ||||||||
\(292\) | 10.8034i | 0.632219i | ||||||||
\(293\) | 17.0284i | 0.994812i | 0.867518 | + | 0.497406i | \(0.165714\pi\) | ||||
−0.867518 | + | 0.497406i | \(0.834286\pi\) | |||||||
\(294\) | 17.7437 | 1.03483 | ||||||||
\(295\) | 7.10250 | + | 4.30498i | 0.413524 | + | 0.250645i | ||||
\(296\) | −2.68411 | −0.156011 | ||||||||
\(297\) | 20.4966i | 1.18934i | ||||||||
\(298\) | 3.76674i | 0.218202i | ||||||||
\(299\) | −0.656620 | −0.0379733 | ||||||||
\(300\) | −17.1377 | + | 8.94343i | −0.989446 | + | 0.516349i | ||||
\(301\) | −2.79432 | −0.161062 | ||||||||
\(302\) | − | 0.170810i | − | 0.00982904i | ||||||
\(303\) | 10.9043i | 0.626437i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 6.71425 | + | 4.06965i | 0.384457 | + | 0.233028i | ||||
\(306\) | 29.6111 | 1.69275 | ||||||||
\(307\) | 20.9793i | 1.19735i | 0.800992 | + | 0.598676i | \(0.204306\pi\) | ||||
−0.800992 | + | 0.598676i | \(0.795694\pi\) | |||||||
\(308\) | 1.36022i | 0.0775058i | ||||||||
\(309\) | −48.3176 | −2.74869 | ||||||||
\(310\) | −5.65662 | + | 9.33249i | −0.321274 | + | 0.530050i | ||||
\(311\) | −3.14805 | −0.178509 | −0.0892547 | − | 0.996009i | \(-0.528449\pi\) | ||||
−0.0892547 | + | 0.996009i | \(0.528449\pi\) | |||||||
\(312\) | 1.68248i | 0.0952520i | ||||||||
\(313\) | − | 12.2928i | − | 0.694831i | −0.937711 | − | 0.347416i | \(-0.887059\pi\) | ||
0.937711 | − | 0.347416i | \(-0.112941\pi\) | |||||||
\(314\) | −13.6060 | −0.767832 | ||||||||
\(315\) | 4.25561 | − | 7.02105i | 0.239776 | − | 0.395592i | ||||
\(316\) | −8.32027 | −0.468052 | ||||||||
\(317\) | − | 11.4619i | − | 0.643765i | −0.946780 | − | 0.321882i | \(-0.895684\pi\) | ||
0.946780 | − | 0.321882i | \(-0.104316\pi\) | |||||||
\(318\) | − | 21.8005i | − | 1.22251i | ||||||
\(319\) | −16.7065 | −0.935387 | ||||||||
\(320\) | 9.05763 | + | 5.49002i | 0.506337 | + | 0.306902i | ||||
\(321\) | 3.25561 | 0.181710 | ||||||||
\(322\) | − | 1.64984i | − | 0.0919417i | ||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 17.0275 | 0.945972 | ||||||||
\(325\) | −0.862301 | + | 0.449998i | −0.0478318 | + | 0.0249614i | ||||
\(326\) | 7.92696 | 0.439034 | ||||||||
\(327\) | 20.7669i | 1.14841i | ||||||||
\(328\) | − | 28.2290i | − | 1.55869i | ||||||
\(329\) | −5.00770 | −0.276084 | ||||||||
\(330\) | 9.71425 | + | 5.88801i | 0.534752 | + | 0.324124i | ||||
\(331\) | 5.85724 | 0.321943 | 0.160972 | − | 0.986959i | \(-0.448537\pi\) | ||||
0.160972 | + | 0.986959i | \(0.448537\pi\) | |||||||
\(332\) | − | 5.67204i | − | 0.311294i | ||||||
\(333\) | 6.19320i | 0.339385i | ||||||||
\(334\) | 2.64892 | 0.144942 | ||||||||
\(335\) | −4.68676 | + | 7.73238i | −0.256065 | + | 0.422465i | ||||
\(336\) | 0.153107 | 0.00835265 | ||||||||
\(337\) | − | 8.60995i | − | 0.469014i | −0.972114 | − | 0.234507i | \(-0.924652\pi\) | ||
0.972114 | − | 0.234507i | \(-0.0753476\pi\) | |||||||
\(338\) | − | 11.1835i | − | 0.608302i | ||||||
\(339\) | 24.3280 | 1.32131 | ||||||||
\(340\) | −7.70655 | + | 12.7145i | −0.417946 | + | 0.689543i | ||||
\(341\) | −10.8168 | −0.585760 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 7.74945i | − | 0.418431i | ||||||
\(344\) | −13.8546 | −0.746990 | ||||||||
\(345\) | 19.8744 | + | 12.0463i | 1.07000 | + | 0.648550i | ||||
\(346\) | 8.98459 | 0.483015 | ||||||||
\(347\) | 12.0901i | 0.649033i | 0.945880 | + | 0.324517i | \(0.105202\pi\) | ||||
−0.945880 | + | 0.324517i | \(0.894798\pi\) | |||||||
\(348\) | 33.7777i | 1.81067i | ||||||||
\(349\) | −18.9819 | −1.01608 | −0.508040 | − | 0.861333i | \(-0.669630\pi\) | ||||
−0.508040 | + | 0.861333i | \(0.669630\pi\) | |||||||
\(350\) | −1.13067 | − | 2.16663i | −0.0604369 | − | 0.115811i | ||||
\(351\) | 2.08513 | 0.111296 | ||||||||
\(352\) | 10.8872i | 0.580292i | ||||||||
\(353\) | − | 7.71759i | − | 0.410766i | −0.978682 | − | 0.205383i | \(-0.934156\pi\) | ||
0.978682 | − | 0.205383i | \(-0.0658440\pi\) | |||||||
\(354\) | −9.86736 | −0.524444 | ||||||||
\(355\) | −9.93466 | − | 6.02161i | −0.527277 | − | 0.319594i | ||||
\(356\) | −4.23582 | −0.224498 | ||||||||
\(357\) | − | 9.23741i | − | 0.488895i | ||||||
\(358\) | − | 11.5986i | − | 0.613003i | ||||||
\(359\) | 7.03014 | 0.371037 | 0.185518 | − | 0.982641i | \(-0.440604\pi\) | ||||
0.185518 | + | 0.982641i | \(0.440604\pi\) | |||||||
\(360\) | 21.0999 | − | 34.8113i | 1.11206 | − | 1.83472i | ||||
\(361\) | 0 | 0 | ||||||||
\(362\) | − | 6.86960i | − | 0.361058i | ||||||
\(363\) | − | 22.6113i | − | 1.18678i | ||||||
\(364\) | 0.138375 | 0.00725284 | ||||||||
\(365\) | 9.97251 | − | 16.4530i | 0.521985 | − | 0.861189i | ||||
\(366\) | −9.32797 | −0.487581 | ||||||||
\(367\) | 33.7109i | 1.75969i | 0.475257 | + | 0.879847i | \(0.342355\pi\) | ||||
−0.475257 | + | 0.879847i | \(0.657645\pi\) | |||||||
\(368\) | 0.296261i | 0.0154437i | ||||||||
\(369\) | −65.1344 | −3.39076 | ||||||||
\(370\) | 1.57655 | + | 0.955582i | 0.0819611 | + | 0.0496784i | ||||
\(371\) | −4.64892 | −0.241360 | ||||||||
\(372\) | 21.8696i | 1.13388i | ||||||||
\(373\) | 10.0097i | 0.518281i | 0.965840 | + | 0.259141i | \(0.0834393\pi\) | ||||
−0.965840 | + | 0.259141i | \(0.916561\pi\) | |||||||
\(374\) | 8.73669 | 0.451763 | ||||||||
\(375\) | 34.3555 | + | 2.19928i | 1.77411 | + | 0.113570i | ||||
\(376\) | −24.8288 | −1.28045 | ||||||||
\(377\) | 1.69956i | 0.0875317i | ||||||||
\(378\) | 5.23912i | 0.269471i | ||||||||
\(379\) | 35.8064 | 1.83925 | 0.919626 | − | 0.392796i | \(-0.128492\pi\) | ||||
0.919626 | + | 0.392796i | \(0.128492\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −26.0999 | −1.33714 | ||||||||
\(382\) | 12.1651i | 0.622420i | ||||||||
\(383\) | − | 16.2495i | − | 0.830312i | −0.909750 | − | 0.415156i | \(-0.863727\pi\) | ||
0.909750 | − | 0.415156i | \(-0.136273\pi\) | |||||||
\(384\) | 22.4784 | 1.14710 | ||||||||
\(385\) | 1.25561 | − | 2.07155i | 0.0639917 | − | 0.105576i | ||||
\(386\) | 3.43115 | 0.174641 | ||||||||
\(387\) | 31.9675i | 1.62500i | ||||||||
\(388\) | − | 19.0755i | − | 0.968411i | ||||||
\(389\) | 19.3856 | 0.982889 | 0.491445 | − | 0.870909i | \(-0.336469\pi\) | ||||
0.491445 | + | 0.870909i | \(0.336469\pi\) | |||||||
\(390\) | 0.598988 | − | 0.988232i | 0.0303310 | − | 0.0500411i | ||||
\(391\) | 17.8744 | 0.903947 | ||||||||
\(392\) | − | 18.7607i | − | 0.947556i | ||||||
\(393\) | 5.77149i | 0.291133i | ||||||||
\(394\) | −15.8315 | −0.797579 | ||||||||
\(395\) | 12.6714 | + | 7.68037i | 0.637565 | + | 0.386442i | ||||
\(396\) | 15.5611 | 0.781977 | ||||||||
\(397\) | − | 5.35414i | − | 0.268717i | −0.990933 | − | 0.134358i | \(-0.957103\pi\) | ||
0.990933 | − | 0.134358i | \(-0.0428973\pi\) | |||||||
\(398\) | − | 1.38622i | − | 0.0694851i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.203035 | + | 0.389063i | 0.0101518 | + | 0.0194531i | ||||
\(401\) | 8.33832 | 0.416396 | 0.208198 | − | 0.978087i | \(-0.433240\pi\) | ||||
0.208198 | + | 0.978087i | \(0.433240\pi\) | |||||||
\(402\) | − | 10.7424i | − | 0.535784i | ||||||
\(403\) | 1.10039i | 0.0548143i | ||||||||
\(404\) | 4.44656 | 0.221225 | ||||||||
\(405\) | −25.9320 | − | 15.7179i | −1.28857 | − | 0.781031i | ||||
\(406\) | −4.27034 | −0.211933 | ||||||||
\(407\) | 1.82729i | 0.0905755i | ||||||||
\(408\) | − | 45.8003i | − | 2.26745i | ||||||
\(409\) | 35.3227 | 1.74659 | 0.873297 | − | 0.487188i | \(-0.161977\pi\) | ||||
0.873297 | + | 0.487188i | \(0.161977\pi\) | |||||||
\(410\) | −10.0499 | + | 16.5807i | −0.496331 | + | 0.818864i | ||||
\(411\) | 38.3702 | 1.89266 | ||||||||
\(412\) | 19.7029i | 0.970694i | ||||||||
\(413\) | 2.10420i | 0.103541i | ||||||||
\(414\) | −18.8744 | −0.927626 | ||||||||
\(415\) | −5.23582 | + | 8.63824i | −0.257016 | + | 0.424034i | ||||
\(416\) | 1.10756 | 0.0543026 | ||||||||
\(417\) | 0.964511i | 0.0472323i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −21.2453 | −1.03790 | −0.518949 | − | 0.854805i | \(-0.673677\pi\) | ||||
−0.518949 | + | 0.854805i | \(0.673677\pi\) | |||||||
\(420\) | −4.18830 | − | 2.53862i | −0.204368 | − | 0.123872i | ||||
\(421\) | −14.8744 | −0.724933 | −0.362467 | − | 0.931997i | \(-0.618065\pi\) | ||||
−0.362467 | + | 0.931997i | \(0.618065\pi\) | |||||||
\(422\) | 5.26284i | 0.256191i | ||||||||
\(423\) | 57.2890i | 2.78548i | ||||||||
\(424\) | −23.0499 | −1.11940 | ||||||||
\(425\) | 23.4734 | − | 12.2497i | 1.13863 | − | 0.594200i | ||||
\(426\) | 13.8020 | 0.668710 | ||||||||
\(427\) | 1.98917i | 0.0962629i | ||||||||
\(428\) | − | 1.32757i | − | 0.0641706i | ||||||
\(429\) | 1.14540 | 0.0553006 | ||||||||
\(430\) | 8.13770 | + | 4.93243i | 0.392435 | + | 0.237863i | ||||
\(431\) | −16.9518 | −0.816540 | −0.408270 | − | 0.912861i | \(-0.633868\pi\) | ||||
−0.408270 | + | 0.912861i | \(0.633868\pi\) | |||||||
\(432\) | − | 0.940790i | − | 0.0452638i | ||||||
\(433\) | 23.1459i | 1.11232i | 0.831075 | + | 0.556161i | \(0.187726\pi\) | ||||
−0.831075 | + | 0.556161i | \(0.812274\pi\) | |||||||
\(434\) | −2.76486 | −0.132717 | ||||||||
\(435\) | 31.1799 | − | 51.4417i | 1.49496 | − | 2.46644i | ||||
\(436\) | 8.46832 | 0.405559 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 22.8578i | 1.09219i | ||||||||
\(439\) | −33.5457 | −1.60105 | −0.800525 | − | 0.599299i | \(-0.795446\pi\) | ||||
−0.800525 | + | 0.599299i | \(0.795446\pi\) | |||||||
\(440\) | 6.22547 | − | 10.2710i | 0.296788 | − | 0.489651i | ||||
\(441\) | −43.2875 | −2.06131 | ||||||||
\(442\) | − | 0.888784i | − | 0.0422752i | ||||||
\(443\) | − | 31.3579i | − | 1.48986i | −0.667144 | − | 0.744929i | \(-0.732483\pi\) | ||
0.667144 | − | 0.744929i | \(-0.267517\pi\) | |||||||
\(444\) | 3.69446 | 0.175331 | ||||||||
\(445\) | 6.45094 | + | 3.91005i | 0.305804 | + | 0.185354i | ||||
\(446\) | 14.8616 | 0.703718 | ||||||||
\(447\) | − | 13.4429i | − | 0.635829i | ||||||
\(448\) | 2.68343i | 0.126780i | ||||||||
\(449\) | 16.0301 | 0.756509 | 0.378255 | − | 0.925702i | \(-0.376524\pi\) | ||||
0.378255 | + | 0.925702i | \(0.376524\pi\) | |||||||
\(450\) | −24.7866 | + | 12.9351i | −1.16845 | + | 0.609765i | ||||
\(451\) | −19.2178 | −0.904929 | ||||||||
\(452\) | − | 9.92045i | − | 0.466619i | ||||||
\(453\) | 0.609597i | 0.0286414i | ||||||||
\(454\) | −1.02243 | −0.0479853 | ||||||||
\(455\) | −0.210739 | − | 0.127733i | −0.00987959 | − | 0.00598823i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 15.3980i | 0.720286i | 0.932897 | + | 0.360143i | \(0.117272\pi\) | ||||
−0.932897 | + | 0.360143i | \(0.882728\pi\) | |||||||
\(458\) | 5.39057i | 0.251885i | ||||||||
\(459\) | −56.7609 | −2.64937 | ||||||||
\(460\) | 4.91223 | − | 8.10437i | 0.229034 | − | 0.377868i | ||||
\(461\) | −5.81411 | −0.270790 | −0.135395 | − | 0.990792i | \(-0.543230\pi\) | ||||
−0.135395 | + | 0.990792i | \(0.543230\pi\) | |||||||
\(462\) | 2.87796i | 0.133895i | ||||||||
\(463\) | − | 32.6788i | − | 1.51871i | −0.650675 | − | 0.759356i | \(-0.725514\pi\) | ||
0.650675 | − | 0.759356i | \(-0.274486\pi\) | |||||||
\(464\) | 0.766826 | 0.0355990 | ||||||||
\(465\) | 20.1876 | − | 33.3063i | 0.936179 | − | 1.54454i | ||||
\(466\) | −2.37858 | −0.110185 | ||||||||
\(467\) | − | 6.59041i | − | 0.304968i | −0.988306 | − | 0.152484i | \(-0.951273\pi\) | ||
0.988306 | − | 0.152484i | \(-0.0487272\pi\) | |||||||
\(468\) | − | 1.58304i | − | 0.0731759i | ||||||
\(469\) | −2.29081 | −0.105780 | ||||||||
\(470\) | 14.5836 | + | 8.83942i | 0.672690 | + | 0.407732i | ||||
\(471\) | 48.5578 | 2.23743 | ||||||||
\(472\) | 10.4329i | 0.480212i | ||||||||
\(473\) | 9.43194i | 0.433681i | ||||||||
\(474\) | −17.6040 | −0.808581 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −3.76683 | −0.172652 | ||||||||
\(477\) | 53.1844i | 2.43515i | ||||||||
\(478\) | 14.9309i | 0.682923i | ||||||||
\(479\) | 36.8064 | 1.68173 | 0.840864 | − | 0.541247i | \(-0.182048\pi\) | ||||
0.840864 | + | 0.541247i | \(0.182048\pi\) | |||||||
\(480\) | −33.5233 | − | 20.3192i | −1.53012 | − | 0.927440i | ||||
\(481\) | 0.185891 | 0.00847588 | ||||||||
\(482\) | 4.12980i | 0.188107i | ||||||||
\(483\) | 5.88801i | 0.267914i | ||||||||
\(484\) | −9.22041 | −0.419110 | ||||||||
\(485\) | −17.6084 | + | 29.0510i | −0.799558 | + | 1.31914i | ||||
\(486\) | 8.28310 | 0.375729 | ||||||||
\(487\) | 2.45475i | 0.111235i | 0.998452 | + | 0.0556176i | \(0.0177128\pi\) | ||||
−0.998452 | + | 0.0556176i | \(0.982287\pi\) | |||||||
\(488\) | 9.86258i | 0.446458i | ||||||||
\(489\) | −28.2901 | −1.27932 | ||||||||
\(490\) | −6.67906 | + | 11.0193i | −0.301729 | + | 0.497803i | ||||
\(491\) | 17.7943 | 0.803046 | 0.401523 | − | 0.915849i | \(-0.368481\pi\) | ||||
0.401523 | + | 0.915849i | \(0.368481\pi\) | |||||||
\(492\) | 38.8549i | 1.75172i | ||||||||
\(493\) | − | 46.2651i | − | 2.08367i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −23.6988 | − | 14.3644i | −1.06518 | − | 0.645630i | ||||
\(496\) | 0.496486 | 0.0222929 | ||||||||
\(497\) | − | 2.94326i | − | 0.132023i | ||||||
\(498\) | − | 12.0009i | − | 0.537774i | ||||||
\(499\) | 29.2798 | 1.31074 | 0.655371 | − | 0.755307i | \(-0.272512\pi\) | ||||
0.655371 | + | 0.755307i | \(0.272512\pi\) | |||||||
\(500\) | 0.896822 | − | 14.0095i | 0.0401071 | − | 0.626522i | ||||
\(501\) | −9.45359 | −0.422355 | ||||||||
\(502\) | 22.6462i | 1.01075i | ||||||||
\(503\) | 29.4378i | 1.31257i | 0.754515 | + | 0.656283i | \(0.227872\pi\) | ||||
−0.754515 | + | 0.656283i | \(0.772128\pi\) | |||||||
\(504\) | 10.3132 | 0.459388 | ||||||||
\(505\) | −6.77188 | − | 4.10458i | −0.301345 | − | 0.182652i | ||||
\(506\) | −5.56885 | −0.247566 | ||||||||
\(507\) | 39.9122i | 1.77257i | ||||||||
\(508\) | 10.6430i | 0.472206i | ||||||||
\(509\) | −6.69446 | −0.296727 | −0.148363 | − | 0.988933i | \(-0.547401\pi\) | ||||
−0.148363 | + | 0.988933i | \(0.547401\pi\) | |||||||
\(510\) | −16.3055 | + | 26.9014i | −0.722021 | + | 1.19122i | ||||
\(511\) | 4.87439 | 0.215630 | ||||||||
\(512\) | − | 0.992797i | − | 0.0438758i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 19.1973 | 0.846757 | ||||||||
\(515\) | 18.1876 | − | 30.0066i | 0.801443 | − | 1.32225i | ||||
\(516\) | 19.0697 | 0.839498 | ||||||||
\(517\) | 16.9030i | 0.743393i | ||||||||
\(518\) | 0.467072i | 0.0205220i | ||||||||
\(519\) | −32.0647 | −1.40748 | ||||||||
\(520\) | −1.04487 | − | 0.633318i | −0.0458206 | − | 0.0277728i | ||||
\(521\) | 20.0801 | 0.879724 | 0.439862 | − | 0.898065i | \(-0.355027\pi\) | ||||
0.439862 | + | 0.898065i | \(0.355027\pi\) | |||||||
\(522\) | 48.8534i | 2.13825i | ||||||||
\(523\) | − | 36.4440i | − | 1.59359i | −0.604252 | − | 0.796793i | \(-0.706528\pi\) | ||
0.604252 | − | 0.796793i | \(-0.293472\pi\) | |||||||
\(524\) | 2.35350 | 0.102813 | ||||||||
\(525\) | 4.03520 | + | 7.73238i | 0.176110 | + | 0.337469i | ||||
\(526\) | 7.60405 | 0.331552 | ||||||||
\(527\) | − | 29.9546i | − | 1.30484i | ||||||
\(528\) | − | 0.516796i | − | 0.0224907i | ||||||
\(529\) | 11.6067 | 0.504639 | ||||||||
\(530\) | 13.5387 | + | 8.20610i | 0.588084 | + | 0.356450i | ||||
\(531\) | 24.0724 | 1.04465 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.95503i | 0.0846816i | ||||||||
\(534\) | −8.96216 | −0.387830 | ||||||||
\(535\) | −1.22547 | + | 2.02182i | −0.0529817 | + | 0.0874111i | ||||
\(536\) | −11.3581 | −0.490596 | ||||||||
\(537\) | 41.3936i | 1.78626i | ||||||||
\(538\) | − | 4.11045i | − | 0.177214i | ||||||
\(539\) | −12.7719 | −0.550124 | ||||||||
\(540\) | −15.5990 | + | 25.7358i | −0.671274 | + | 1.10749i | ||||
\(541\) | −14.6291 | −0.628955 | −0.314478 | − | 0.949265i | \(-0.601829\pi\) | ||||
−0.314478 | + | 0.949265i | \(0.601829\pi\) | |||||||
\(542\) | − | 3.03606i | − | 0.130410i | ||||||
\(543\) | 24.5166i | 1.05211i | ||||||||
\(544\) | −30.1498 | −1.29266 | ||||||||
\(545\) | −12.8968 | − | 7.81704i | −0.552439 | − | 0.334845i | ||||
\(546\) | 0.292775 | 0.0125296 | ||||||||
\(547\) | − | 20.4186i | − | 0.873038i | −0.899695 | − | 0.436519i | \(-0.856211\pi\) | ||
0.899695 | − | 0.436519i | \(-0.143789\pi\) | |||||||
\(548\) | − | 15.6466i | − | 0.668389i | ||||||
\(549\) | 22.7565 | 0.971223 | ||||||||
\(550\) | −7.31324 | + | 3.81647i | −0.311838 | + | 0.162735i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 29.1935i | 1.24256i | ||||||||
\(553\) | 3.75403i | 0.159638i | ||||||||
\(554\) | −28.2754 | −1.20131 | ||||||||
\(555\) | −5.62648 | − | 3.41033i | −0.238831 | − | 0.144760i | ||||
\(556\) | 0.393308 | 0.0166800 | ||||||||
\(557\) | − | 35.8798i | − | 1.52028i | −0.649761 | − | 0.760138i | \(-0.725131\pi\) | ||
0.649761 | − | 0.760138i | \(-0.274869\pi\) | |||||||
\(558\) | 31.6304i | 1.33902i | ||||||||
\(559\) | 0.959512 | 0.0405830 | ||||||||
\(560\) | −0.0576321 | + | 0.0950835i | −0.00243540 | + | 0.00401801i | ||||
\(561\) | −31.1799 | −1.31642 | ||||||||
\(562\) | − | 8.55873i | − | 0.361028i | ||||||
\(563\) | 37.7708i | 1.59185i | 0.605395 | + | 0.795925i | \(0.293015\pi\) | ||||
−0.605395 | + | 0.795925i | \(0.706985\pi\) | |||||||
\(564\) | 34.1749 | 1.43902 | ||||||||
\(565\) | −9.15749 | + | 15.1083i | −0.385258 | + | 0.635613i | ||||
\(566\) | −2.13264 | −0.0896416 | ||||||||
\(567\) | − | 7.68266i | − | 0.322641i | ||||||
\(568\) | − | 14.5931i | − | 0.612311i | ||||||
\(569\) | −28.0844 | −1.17736 | −0.588681 | − | 0.808366i | \(-0.700352\pi\) | ||||
−0.588681 | + | 0.808366i | \(0.700352\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 20.6040 | 0.862253 | 0.431126 | − | 0.902292i | \(-0.358116\pi\) | ||||
0.431126 | + | 0.902292i | \(0.358116\pi\) | |||||||
\(572\) | − | 0.467072i | − | 0.0195293i | ||||||
\(573\) | − | 43.4154i | − | 1.81370i | ||||||
\(574\) | −4.91223 | −0.205032 | ||||||||
\(575\) | −14.9622 | + | 7.80811i | −0.623965 | + | 0.325621i | ||||
\(576\) | 30.6988 | 1.27912 | ||||||||
\(577\) | 43.8371i | 1.82496i | 0.409119 | + | 0.912481i | \(0.365836\pi\) | ||||
−0.409119 | + | 0.912481i | \(0.634164\pi\) | |||||||
\(578\) | 9.52702i | 0.396272i | ||||||||
\(579\) | −12.2453 | −0.508896 | ||||||||
\(580\) | −20.9769 | − | 12.7145i | −0.871018 | − | 0.527942i | ||||
\(581\) | −2.55918 | −0.106173 | ||||||||
\(582\) | − | 40.3600i | − | 1.67297i | ||||||
\(583\) | 15.6919i | 0.649894i | ||||||||
\(584\) | 24.1678 | 1.00007 | ||||||||
\(585\) | −1.46129 | + | 2.41089i | −0.0604169 | + | 0.0996779i | ||||
\(586\) | 14.6918 | 0.606913 | ||||||||
\(587\) | 37.9809i | 1.56764i | 0.620987 | + | 0.783821i | \(0.286732\pi\) | ||||
−0.620987 | + | 0.783821i | \(0.713268\pi\) | |||||||
\(588\) | 25.8225i | 1.06490i | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 3.71425 | − | 6.12790i | 0.152913 | − | 0.252282i | ||||
\(591\) | 56.5002 | 2.32411 | ||||||||
\(592\) | − | 0.0838722i | − | 0.00344713i | ||||||
\(593\) | 5.38015i | 0.220936i | 0.993880 | + | 0.110468i | \(0.0352350\pi\) | ||||
−0.993880 | + | 0.110468i | \(0.964765\pi\) | |||||||
\(594\) | 17.6841 | 0.725588 | ||||||||
\(595\) | 5.73669 | + | 3.47713i | 0.235181 | + | 0.142548i | ||||
\(596\) | −5.48175 | −0.224541 | ||||||||
\(597\) | 4.94722i | 0.202476i | ||||||||
\(598\) | 0.566520i | 0.0231667i | ||||||||
\(599\) | −22.4285 | −0.916404 | −0.458202 | − | 0.888848i | \(-0.651506\pi\) | ||||
−0.458202 | + | 0.888848i | \(0.651506\pi\) | |||||||
\(600\) | 20.0070 | + | 38.3381i | 0.816783 | + | 1.56515i | ||||
\(601\) | −29.5732 | −1.20632 | −0.603159 | − | 0.797621i | \(-0.706091\pi\) | ||||
−0.603159 | + | 0.797621i | \(0.706091\pi\) | |||||||
\(602\) | 2.41089i | 0.0982604i | ||||||||
\(603\) | 26.2072i | 1.06724i | ||||||||
\(604\) | 0.248581 | 0.0101146 | ||||||||
\(605\) | 14.0422 | + | 8.51129i | 0.570898 | + | 0.346033i | ||||
\(606\) | 9.40804 | 0.382175 | ||||||||
\(607\) | 24.5915i | 0.998139i | 0.866562 | + | 0.499069i | \(0.166325\pi\) | ||||
−0.866562 | + | 0.499069i | \(0.833675\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 15.2402 | 0.617564 | ||||||||
\(610\) | 3.51122 | − | 5.79293i | 0.142165 | − | 0.234549i | ||||
\(611\) | 1.71954 | 0.0695653 | ||||||||
\(612\) | 43.0931i | 1.74194i | ||||||||
\(613\) | − | 29.8901i | − | 1.20725i | −0.797269 | − | 0.603624i | \(-0.793723\pi\) | ||
0.797269 | − | 0.603624i | \(-0.206277\pi\) | |||||||
\(614\) | 18.1005 | 0.730478 | ||||||||
\(615\) | 35.8667 | − | 59.1741i | 1.44628 | − | 2.38613i | ||||
\(616\) | 3.04290 | 0.122602 | ||||||||
\(617\) | 40.7141i | 1.63909i | 0.573017 | + | 0.819544i | \(0.305773\pi\) | ||||
−0.573017 | + | 0.819544i | \(0.694227\pi\) | |||||||
\(618\) | 41.6875i | 1.67692i | ||||||||
\(619\) | 28.4784 | 1.14464 | 0.572322 | − | 0.820029i | \(-0.306043\pi\) | ||||
0.572322 | + | 0.820029i | \(0.306043\pi\) | |||||||
\(620\) | −13.5816 | − | 8.23210i | −0.545451 | − | 0.330609i | ||||
\(621\) | 36.1799 | 1.45185 | ||||||||
\(622\) | 2.71608i | 0.108905i | ||||||||
\(623\) | 1.91116i | 0.0765692i | ||||||||
\(624\) | −0.0525737 | −0.00210463 | ||||||||
\(625\) | −14.2978 | + | 20.5079i | −0.571913 | + | 0.820314i | ||||
\(626\) | −10.6060 | −0.423902 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 19.8009i | − | 0.790141i | ||||||
\(629\) | −5.06028 | −0.201766 | ||||||||
\(630\) | −6.05763 | − | 3.67166i | −0.241342 | − | 0.146282i | ||||
\(631\) | 42.4201 | 1.68872 | 0.844359 | − | 0.535777i | \(-0.179981\pi\) | ||||
0.844359 | + | 0.535777i | \(0.179981\pi\) | |||||||
\(632\) | 18.6130i | 0.740384i | ||||||||
\(633\) | − | 18.7823i | − | 0.746529i | ||||||
\(634\) | −9.88912 | −0.392747 | ||||||||
\(635\) | 9.82446 | − | 16.2087i | 0.389872 | − | 0.643224i | ||||
\(636\) | 31.7263 | 1.25803 | ||||||||
\(637\) | 1.29929i | 0.0514796i | ||||||||
\(638\) | 14.4141i | 0.570659i | ||||||||
\(639\) | −33.6714 | −1.33202 | ||||||||
\(640\) | −8.46129 | + | 13.9597i | −0.334462 | + | 0.551807i | ||||
\(641\) | −29.5259 | −1.16620 | −0.583102 | − | 0.812399i | \(-0.698161\pi\) | ||||
−0.583102 | + | 0.812399i | \(0.698161\pi\) | |||||||
\(642\) | − | 2.80888i | − | 0.110858i | ||||||
\(643\) | 21.5970i | 0.851704i | 0.904793 | + | 0.425852i | \(0.140026\pi\) | ||||
−0.904793 | + | 0.425852i | \(0.859974\pi\) | |||||||
\(644\) | 2.40101 | 0.0946131 | ||||||||
\(645\) | −29.0422 | − | 17.6031i | −1.14354 | − | 0.693122i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 12.6128i | 0.495861i | 0.968778 | + | 0.247930i | \(0.0797504\pi\) | ||||
−0.968778 | + | 0.247930i | \(0.920250\pi\) | |||||||
\(648\) | − | 38.0916i | − | 1.49638i | ||||||
\(649\) | 7.10250 | 0.278798 | ||||||||
\(650\) | 0.388250 | + | 0.743977i | 0.0152284 | + | 0.0291812i | ||||
\(651\) | 9.86736 | 0.386732 | ||||||||
\(652\) | 11.5361i | 0.451790i | ||||||||
\(653\) | − | 26.6312i | − | 1.04216i | −0.853508 | − | 0.521080i | \(-0.825529\pi\) | ||
0.853508 | − | 0.521080i | \(-0.174471\pi\) | |||||||
\(654\) | 17.9173 | 0.700621 | ||||||||
\(655\) | −3.58426 | − | 2.17249i | −0.140049 | − | 0.0848864i | ||||
\(656\) | 0.882090 | 0.0344398 | ||||||||
\(657\) | − | 55.7638i | − | 2.17555i | ||||||
\(658\) | 4.32055i | 0.168433i | ||||||||
\(659\) | −39.9545 | −1.55640 | −0.778202 | − | 0.628014i | \(-0.783868\pi\) | ||||
−0.778202 | + | 0.628014i | \(0.783868\pi\) | |||||||
\(660\) | −8.56885 | + | 14.1372i | −0.333542 | + | 0.550289i | ||||
\(661\) | −13.5233 | −0.525996 | −0.262998 | − | 0.964796i | \(-0.584711\pi\) | ||||
−0.262998 | + | 0.964796i | \(0.584711\pi\) | |||||||
\(662\) | − | 5.05352i | − | 0.196411i | ||||||
\(663\) | 3.17194i | 0.123188i | ||||||||
\(664\) | −12.6887 | −0.492418 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 5.34338 | 0.207052 | ||||||||
\(667\) | 29.4898i | 1.14185i | ||||||||
\(668\) | 3.85498i | 0.149154i | ||||||||
\(669\) | −53.0389 | −2.05060 | ||||||||
\(670\) | 6.67135 | + | 4.04365i | 0.257737 | + | 0.156220i | ||||
\(671\) | 6.71425 | 0.259201 | ||||||||
\(672\) | − | 9.93166i | − | 0.383122i | ||||||
\(673\) | 34.4110i | 1.32645i | 0.748421 | + | 0.663224i | \(0.230812\pi\) | ||||
−0.748421 | + | 0.663224i | \(0.769188\pi\) | |||||||
\(674\) | −7.42851 | −0.286135 | ||||||||
\(675\) | 47.5130 | − | 24.7950i | 1.82877 | − | 0.954359i | ||||
\(676\) | 16.2754 | 0.625977 | ||||||||
\(677\) | 29.6650i | 1.14012i | 0.821604 | + | 0.570059i | \(0.193080\pi\) | ||||
−0.821604 | + | 0.570059i | \(0.806920\pi\) | |||||||
\(678\) | − | 20.9897i | − | 0.806105i | ||||||
\(679\) | −8.60669 | −0.330295 | ||||||||
\(680\) | 28.4432 | + | 17.2400i | 1.09075 | + | 0.661126i | ||||
\(681\) | 3.64892 | 0.139827 | ||||||||
\(682\) | 9.33249i | 0.357360i | ||||||||
\(683\) | − | 27.8978i | − | 1.06748i | −0.845648 | − | 0.533740i | \(-0.820786\pi\) | ||
0.845648 | − | 0.533740i | \(-0.179214\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −14.4432 | + | 23.8290i | −0.551848 | + | 0.910458i | ||||
\(686\) | −6.68608 | −0.255276 | ||||||||
\(687\) | − | 19.2381i | − | 0.733981i | ||||||
\(688\) | − | 0.432924i | − | 0.0165051i | ||||||
\(689\) | 1.59634 | 0.0608158 | ||||||||
\(690\) | 10.3933 | − | 17.1472i | 0.395666 | − | 0.652784i | ||||
\(691\) | −49.6386 | −1.88834 | −0.944170 | − | 0.329459i | \(-0.893134\pi\) | ||||
−0.944170 | + | 0.329459i | \(0.893134\pi\) | |||||||
\(692\) | 13.0753i | 0.497049i | ||||||||
\(693\) | − | 7.02105i | − | 0.266708i | ||||||
\(694\) | 10.4312 | 0.395961 | ||||||||
\(695\) | −0.598988 | − | 0.363059i | −0.0227209 | − | 0.0137716i | ||||
\(696\) | 75.5629 | 2.86420 | ||||||||
\(697\) | − | 53.2193i | − | 2.01582i | ||||||
\(698\) | 16.3773i | 0.619889i | ||||||||
\(699\) | 8.48878 | 0.321075 | ||||||||
\(700\) | 3.15311 | − | 1.64547i | 0.119176 | − | 0.0621930i | ||||
\(701\) | −49.9813 | −1.88777 | −0.943883 | − | 0.330279i | \(-0.892857\pi\) | ||||
−0.943883 | + | 0.330279i | \(0.892857\pi\) | |||||||
\(702\) | − | 1.79901i | − | 0.0678991i | ||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 9.05763 | 0.341372 | ||||||||
\(705\) | −52.0466 | − | 31.5465i | −1.96019 | − | 1.18811i | ||||
\(706\) | −6.65859 | −0.250599 | ||||||||
\(707\) | − | 2.00625i | − | 0.0754527i | ||||||
\(708\) | − | 14.3600i | − | 0.539682i | ||||||
\(709\) | −25.1876 | −0.945941 | −0.472971 | − | 0.881078i | \(-0.656818\pi\) | ||||
−0.472971 | + | 0.881078i | \(0.656818\pi\) | |||||||
\(710\) | −5.19533 | + | 8.57144i | −0.194977 | + | 0.321680i | ||||
\(711\) | 42.9468 | 1.61063 | ||||||||
\(712\) | 9.47580i | 0.355121i | ||||||||
\(713\) | 19.0933i | 0.715051i | ||||||||
\(714\) | −7.96986 | −0.298265 | ||||||||
\(715\) | −0.431150 | + | 0.711327i | −0.0161241 | + | 0.0266021i | ||||
\(716\) | 16.8794 | 0.630814 | ||||||||
\(717\) | − | 53.2861i | − | 1.99001i | ||||||
\(718\) | − | 6.06547i | − | 0.226361i | ||||||
\(719\) | −17.1755 | −0.640540 | −0.320270 | − | 0.947326i | \(-0.603774\pi\) | ||||
−0.320270 | + | 0.947326i | \(0.603774\pi\) | |||||||
\(720\) | 1.08777 | + | 0.659321i | 0.0405388 | + | 0.0245714i | ||||
\(721\) | 8.88979 | 0.331073 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 14.7386i | − | 0.548136i | ||||||
\(724\) | 9.99735 | 0.371549 | ||||||||
\(725\) | 20.2101 | + | 38.7272i | 0.750583 | + | 1.43829i | ||||
\(726\) | −19.5086 | −0.724031 | ||||||||
\(727\) | 1.05653i | 0.0391845i | 0.999808 | + | 0.0195922i | \(0.00623680\pi\) | ||||
−0.999808 | + | 0.0195922i | \(0.993763\pi\) | |||||||
\(728\) | − | 0.309555i | − | 0.0114729i | ||||||
\(729\) | 11.1223 | 0.411937 | ||||||||
\(730\) | −14.1953 | − | 8.60409i | −0.525393 | − | 0.318452i | ||||
\(731\) | −26.1196 | −0.966070 | ||||||||
\(732\) | − | 13.5750i | − | 0.501748i | ||||||
\(733\) | 20.5025i | 0.757277i | 0.925545 | + | 0.378639i | \(0.123608\pi\) | ||||
−0.925545 | + | 0.378639i | \(0.876392\pi\) | |||||||
\(734\) | 29.0851 | 1.07355 | ||||||||
\(735\) | 23.8365 | − | 39.3264i | 0.879224 | − | 1.45058i | ||||
\(736\) | 19.2178 | 0.708376 | ||||||||
\(737\) | 7.73238i | 0.284826i | ||||||||
\(738\) | 56.1967i | 2.06863i | ||||||||
\(739\) | −24.9096 | −0.916314 | −0.458157 | − | 0.888871i | \(-0.651490\pi\) | ||||
−0.458157 | + | 0.888871i | \(0.651490\pi\) | |||||||
\(740\) | −1.39066 | + | 2.29436i | −0.0511218 | + | 0.0843425i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 4.01100i | 0.147248i | ||||||||
\(743\) | 13.2573i | 0.486364i | 0.969981 | + | 0.243182i | \(0.0781913\pi\) | ||||
−0.969981 | + | 0.243182i | \(0.921809\pi\) | |||||||
\(744\) | 48.9236 | 1.79363 | ||||||||
\(745\) | 8.34844 | + | 5.06016i | 0.305863 | + | 0.185390i | ||||
\(746\) | 8.63615 | 0.316192 | ||||||||
\(747\) | 29.2774i | 1.07120i | ||||||||
\(748\) | 12.7145i | 0.464889i | ||||||||
\(749\) | −0.598988 | −0.0218866 | ||||||||
\(750\) | 1.89750 | − | 29.6412i | 0.0692868 | − | 1.08235i | ||||
\(751\) | 24.8365 | 0.906298 | 0.453149 | − | 0.891435i | \(-0.350300\pi\) | ||||
0.453149 | + | 0.891435i | \(0.350300\pi\) | |||||||
\(752\) | − | 0.775843i | − | 0.0282921i | ||||||
\(753\) | − | 80.8209i | − | 2.94528i | ||||||
\(754\) | 1.46635 | 0.0534012 | ||||||||
\(755\) | −0.378577 | − | 0.229463i | −0.0137778 | − | 0.00835103i | ||||
\(756\) | −7.62451 | −0.277301 | ||||||||
\(757\) | − | 48.4658i | − | 1.76152i | −0.473562 | − | 0.880760i | \(-0.657032\pi\) | ||
0.473562 | − | 0.880760i | \(-0.342968\pi\) | |||||||
\(758\) | − | 30.8931i | − | 1.12209i | ||||||
\(759\) | 19.8744 | 0.721395 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 40.3726 | 1.46351 | 0.731753 | − | 0.681570i | \(-0.238702\pi\) | ||||
0.731753 | + | 0.681570i | \(0.238702\pi\) | |||||||
\(762\) | 22.5185i | 0.815758i | ||||||||
\(763\) | − | 3.82083i | − | 0.138323i | ||||||
\(764\) | −17.7039 | −0.640505 | ||||||||
\(765\) | 39.7789 | − | 65.6287i | 1.43821 | − | 2.37281i | ||||
\(766\) | −14.0198 | −0.506556 | ||||||||
\(767\) | − | 0.722538i | − | 0.0260893i | ||||||
\(768\) | − | 48.5638i | − | 1.75239i | ||||||
\(769\) | 44.9545 | 1.62110 | 0.810550 | − | 0.585670i | \(-0.199169\pi\) | ||||
0.810550 | + | 0.585670i | \(0.199169\pi\) | |||||||
\(770\) | −1.78729 | − | 1.08332i | −0.0644095 | − | 0.0390400i | ||||
\(771\) | −68.5123 | −2.46741 | ||||||||
\(772\) | 4.99337i | 0.179715i | ||||||||
\(773\) | 3.68645i | 0.132592i | 0.997800 | + | 0.0662962i | \(0.0211182\pi\) | ||||
−0.997800 | + | 0.0662962i | \(0.978882\pi\) | |||||||
\(774\) | 27.5809 | 0.991376 | ||||||||
\(775\) | 13.0851 | + | 25.0742i | 0.470032 | + | 0.900690i | ||||
\(776\) | −42.6731 | −1.53187 | ||||||||
\(777\) | − | 1.66691i | − | 0.0598000i | ||||||
\(778\) | − | 16.7255i | − | 0.599639i | ||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 1.43818 | + | 0.871710i | 0.0514950 | + | 0.0312122i | ||||
\(781\) | −9.93466 | −0.355490 | ||||||||
\(782\) | − | 15.4217i | − | 0.551478i | ||||||
\(783\) | − | 93.6461i | − | 3.34664i | ||||||
\(784\) | 0.586226 | 0.0209366 | ||||||||
\(785\) | −18.2780 | + | 30.1558i | −0.652371 | + | 1.07631i | ||||
\(786\) | 4.97953 | 0.177614 | ||||||||
\(787\) | − | 45.7141i | − | 1.62953i | −0.579790 | − | 0.814766i | \(-0.696865\pi\) | ||
0.579790 | − | 0.814766i | \(-0.303135\pi\) | |||||||
\(788\) | − | 23.0396i | − | 0.820753i | ||||||
\(789\) | −27.1377 | −0.966128 | ||||||||
\(790\) | 6.62648 | − | 10.9326i | 0.235760 | − | 0.388965i | ||||
\(791\) | −4.47602 | −0.159149 | ||||||||
\(792\) | − | 34.8113i | − | 1.23697i | ||||||
\(793\) | − | 0.683042i | − | 0.0242555i | ||||||
\(794\) | −4.61945 | −0.163938 | ||||||||
\(795\) | −48.3176 | − | 29.2863i | −1.71365 | − | 1.03868i | ||||
\(796\) | 2.01738 | 0.0715040 | ||||||||
\(797\) | 30.3378i | 1.07462i | 0.843385 | + | 0.537310i | \(0.180559\pi\) | ||||
−0.843385 | + | 0.537310i | \(0.819441\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −46.8091 | −1.65599 | ||||||||
\(800\) | 25.2376 | − | 13.1704i | 0.892282 | − | 0.465644i | ||||
\(801\) | 21.8640 | 0.772528 | ||||||||
\(802\) | − | 7.19415i | − | 0.254034i | ||||||
\(803\) | − | 16.4530i | − | 0.580614i | ||||||
\(804\) | 15.6335 | 0.551351 | ||||||||
\(805\) | −3.65662 | − | 2.21635i | −0.128879 | − | 0.0781162i | ||||
\(806\) | 0.949395 | 0.0334410 | ||||||||
\(807\) | 14.6696i | 0.516393i | ||||||||
\(808\) | − | 9.94724i | − | 0.349943i | ||||||
\(809\) | −34.5585 | −1.21501 | −0.607506 | − | 0.794315i | \(-0.707830\pi\) | ||||
−0.607506 | + | 0.794315i | \(0.707830\pi\) | |||||||
\(810\) | −13.5611 | + | 22.3737i | −0.476490 | + | 0.786130i | ||||
\(811\) | 33.2754 | 1.16846 | 0.584229 | − | 0.811589i | \(-0.301397\pi\) | ||||
0.584229 | + | 0.811589i | \(0.301397\pi\) | |||||||
\(812\) | − | 6.21464i | − | 0.218091i | ||||||
\(813\) | 10.8352i | 0.380008i | ||||||||
\(814\) | 1.57655 | 0.0552582 | ||||||||
\(815\) | 10.6489 | − | 17.5690i | 0.373015 | − | 0.615414i | ||||
\(816\) | 1.43115 | 0.0501003 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | − | 30.4757i | − | 1.06556i | ||||||
\(819\) | −0.714253 | −0.0249580 | ||||||||
\(820\) | −24.1300 | − | 14.6257i | −0.842656 | − | 0.510752i | ||||
\(821\) | 12.7013 | 0.443277 | 0.221638 | − | 0.975129i | \(-0.428860\pi\) | ||||
0.221638 | + | 0.975129i | \(0.428860\pi\) | |||||||
\(822\) | − | 33.1051i | − | 1.15467i | ||||||
\(823\) | − | 12.0091i | − | 0.418610i | −0.977850 | − | 0.209305i | \(-0.932880\pi\) | ||
0.977850 | − | 0.209305i | \(-0.0671201\pi\) | |||||||
\(824\) | 44.0767 | 1.53549 | ||||||||
\(825\) | 26.0999 | − | 13.6204i | 0.908680 | − | 0.474201i | ||||
\(826\) | 1.81546 | 0.0631680 | ||||||||
\(827\) | − | 8.54544i | − | 0.297154i | −0.988901 | − | 0.148577i | \(-0.952531\pi\) | ||
0.988901 | − | 0.148577i | \(-0.0474693\pi\) | |||||||
\(828\) | − | 27.4680i | − | 0.954578i | ||||||
\(829\) | 27.1042 | 0.941369 | 0.470685 | − | 0.882302i | \(-0.344007\pi\) | ||||
0.470685 | + | 0.882302i | \(0.344007\pi\) | |||||||
\(830\) | 7.45291 | + | 4.51737i | 0.258694 | + | 0.156800i | ||||
\(831\) | 100.911 | 3.50055 | ||||||||
\(832\) | − | 0.921434i | − | 0.0319450i | ||||||
\(833\) | − | 35.3689i | − | 1.22546i | ||||||
\(834\) | 0.832162 | 0.0288154 | ||||||||
\(835\) | 3.55850 | − | 5.87094i | 0.123147 | − | 0.203172i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 60.6317i | − | 2.09574i | ||||||
\(838\) | 18.3300i | 0.633200i | ||||||||
\(839\) | 36.4379 | 1.25798 | 0.628989 | − | 0.777414i | \(-0.283469\pi\) | ||||
0.628989 | + | 0.777414i | \(0.283469\pi\) | |||||||
\(840\) | −5.67906 | + | 9.36951i | −0.195946 | + | 0.323279i | ||||
\(841\) | 47.3297 | 1.63206 | ||||||||
\(842\) | 12.8333i | 0.442266i | ||||||||
\(843\) | 30.5448i | 1.05202i | ||||||||
\(844\) | −7.65903 | −0.263635 | ||||||||
\(845\) | −24.7866 | − | 15.0237i | −0.852686 | − | 0.516831i | ||||
\(846\) | 49.4278 | 1.69936 | ||||||||
\(847\) | 4.16017i | 0.142945i | ||||||||
\(848\) | − | 0.720256i | − | 0.0247337i | ||||||
\(849\) | 7.61107 | 0.261211 | ||||||||
\(850\) | −10.5688 | − | 20.2524i | −0.362509 | − | 0.694651i | ||||
\(851\) | 3.22547 | 0.110568 | ||||||||
\(852\) | 20.0861i | 0.688140i | ||||||||
\(853\) | − | 18.3471i | − | 0.628192i | −0.949391 | − | 0.314096i | \(-0.898299\pi\) | ||
0.949391 | − | 0.314096i | \(-0.101701\pi\) | |||||||
\(854\) | 1.71622 | 0.0587279 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.96986 | −0.101508 | ||||||||
\(857\) | 7.85783i | 0.268418i | 0.990953 | + | 0.134209i | \(0.0428494\pi\) | ||||
−0.990953 | + | 0.134209i | \(0.957151\pi\) | |||||||
\(858\) | − | 0.988232i | − | 0.0337377i | ||||||
\(859\) | 34.3022 | 1.17038 | 0.585188 | − | 0.810897i | \(-0.301021\pi\) | ||||
0.585188 | + | 0.810897i | \(0.301021\pi\) | |||||||
\(860\) | −7.17819 | + | 11.8428i | −0.244774 | + | 0.403837i | ||||
\(861\) | 17.5310 | 0.597455 | ||||||||
\(862\) | 14.6257i | 0.498153i | ||||||||
\(863\) | − | 35.9451i | − | 1.22359i | −0.791018 | − | 0.611793i | \(-0.790449\pi\) | ||
0.791018 | − | 0.611793i | \(-0.209551\pi\) | |||||||
\(864\) | −61.0268 | −2.07617 | ||||||||
\(865\) | 12.0697 | − | 19.9130i | 0.410383 | − | 0.677064i | ||||
\(866\) | 19.9699 | 0.678604 | ||||||||
\(867\) | − | 34.0005i | − | 1.15472i | ||||||
\(868\) | − | 4.02371i | − | 0.136574i | ||||||
\(869\) | 12.6714 | 0.429846 | ||||||||
\(870\) | −44.3830 | − | 26.9014i | −1.50472 | − | 0.912045i | ||||
\(871\) | 0.786616 | 0.0266535 | ||||||||
\(872\) | − | 18.9442i | − | 0.641531i | ||||||
\(873\) | 98.4620i | 3.33243i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −6.32094 | − | 0.404638i | −0.213687 | − | 0.0136793i | ||||
\(876\) | −33.2650 | −1.12392 | ||||||||
\(877\) | 25.2516i | 0.852686i | 0.904561 | + | 0.426343i | \(0.140198\pi\) | ||||
−0.904561 | + | 0.426343i | \(0.859802\pi\) | |||||||
\(878\) | 28.9426i | 0.976766i | ||||||||
\(879\) | −52.4329 | −1.76852 | ||||||||
\(880\) | 0.320945 | + | 0.194531i | 0.0108190 | + | 0.00655765i | ||||
\(881\) | 17.7796 | 0.599010 | 0.299505 | − | 0.954095i | \(-0.403179\pi\) | ||||
0.299505 | + | 0.954095i | \(0.403179\pi\) | |||||||
\(882\) | 37.3476i | 1.25756i | ||||||||
\(883\) | 7.55342i | 0.254193i | 0.991890 | + | 0.127096i | \(0.0405658\pi\) | ||||
−0.991890 | + | 0.127096i | \(0.959434\pi\) | |||||||
\(884\) | 1.29345 | 0.0435035 | ||||||||
\(885\) | −13.2556 | + | 21.8696i | −0.445582 | + | 0.735138i | ||||
\(886\) | −27.0550 | −0.908930 | ||||||||
\(887\) | 16.2406i | 0.545306i | 0.962112 | + | 0.272653i | \(0.0879011\pi\) | ||||
−0.962112 | + | 0.272653i | \(0.912099\pi\) | |||||||
\(888\) | − | 8.26475i | − | 0.277347i | ||||||
\(889\) | 4.80202 | 0.161055 | ||||||||
\(890\) | 3.37352 | − | 5.56575i | 0.113081 | − | 0.186564i | ||||
\(891\) | −25.9320 | −0.868755 | ||||||||
\(892\) | 21.6282i | 0.724165i | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −11.5983 | −0.387906 | ||||||||
\(895\) | −25.7065 | − | 15.5813i | −0.859275 | − | 0.520825i | ||||
\(896\) | −4.13573 | −0.138165 | ||||||||
\(897\) | − | 2.02182i | − | 0.0675067i | ||||||
\(898\) | − | 13.8305i | − | 0.461530i | ||||||
\(899\) | 49.4201 | 1.64825 | ||||||||
\(900\) | −18.8245 | − | 36.0721i | −0.627482 | − | 1.20240i | ||||
\(901\) | −43.4553 | −1.44771 | ||||||||
\(902\) | 16.5807i | 0.552078i | ||||||||
\(903\) | − | 8.60409i | − | 0.286326i | ||||||
\(904\) | −22.1927 | −0.738118 | ||||||||
\(905\) | −15.2255 | − | 9.22848i | −0.506112 | − | 0.306765i | ||||
\(906\) | 0.525949 | 0.0174735 | ||||||||
\(907\) | 18.2535i | 0.606097i | 0.952975 | + | 0.303049i | \(0.0980045\pi\) | ||||
−0.952975 | + | 0.303049i | \(0.901996\pi\) | |||||||
\(908\) | − | 1.48795i | − | 0.0493795i | ||||||
\(909\) | −22.9518 | −0.761263 | ||||||||
\(910\) | −0.110206 | + | 0.181821i | −0.00365329 | + | 0.00602732i | ||||
\(911\) | 15.9019 | 0.526853 | 0.263426 | − | 0.964679i | \(-0.415147\pi\) | ||||
0.263426 | + | 0.964679i | \(0.415147\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8.63824i | 0.285884i | ||||||||
\(914\) | 13.2851 | 0.439431 | ||||||||
\(915\) | −12.5310 | + | 20.6741i | −0.414262 | + | 0.683465i | ||||
\(916\) | −7.84492 | −0.259204 | ||||||||
\(917\) | − | 1.06188i | − | 0.0350663i | ||||||
\(918\) | 48.9722i | 1.61632i | ||||||||
\(919\) | 30.0748 | 0.992075 | 0.496038 | − | 0.868301i | \(-0.334788\pi\) | ||||
0.496038 | + | 0.868301i | \(0.334788\pi\) | |||||||
\(920\) | −18.1300 | − | 10.9890i | −0.597728 | − | 0.362296i | ||||
\(921\) | −64.5981 | −2.12858 | ||||||||
\(922\) | 5.01630i | 0.165203i | ||||||||
\(923\) | 1.01065i | 0.0332661i | ||||||||
\(924\) | −4.18830 | −0.137785 | ||||||||
\(925\) | 4.23582 | − | 2.21049i | 0.139273 | − | 0.0726805i | ||||
\(926\) | −28.1947 | −0.926534 | ||||||||
\(927\) | − | 101.701i | − | 3.34029i | ||||||
\(928\) | − | 49.7422i | − | 1.63287i | ||||||
\(929\) | 36.8442 | 1.20882 | 0.604410 | − | 0.796673i | \(-0.293409\pi\) | ||||
0.604410 | + | 0.796673i | \(0.293409\pi\) | |||||||
\(930\) | −28.7360 | − | 17.4175i | −0.942291 | − | 0.571142i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | − | 3.46155i | − | 0.113387i | ||||||
\(933\) | − | 9.69327i | − | 0.317343i | ||||||
\(934\) | −5.68608 | −0.186054 | ||||||||
\(935\) | 11.7367 | − | 19.3636i | 0.383831 | − | 0.633257i | ||||
\(936\) | −3.54136 | −0.115753 | ||||||||
\(937\) | 43.2321i | 1.41233i | 0.708047 | + | 0.706165i | \(0.249576\pi\) | ||||
−0.708047 | + | 0.706165i | \(0.750424\pi\) | |||||||
\(938\) | 1.97646i | 0.0645338i | ||||||||
\(939\) | 37.8513 | 1.23523 | ||||||||
\(940\) | −12.8640 | + | 21.2235i | −0.419579 | + | 0.692236i | ||||
\(941\) | −20.3203 | −0.662422 | −0.331211 | − | 0.943557i | \(-0.607457\pi\) | ||||
−0.331211 | + | 0.943557i | \(0.607457\pi\) | |||||||
\(942\) | − | 41.8948i | − | 1.36501i | ||||||
\(943\) | 33.9225i | 1.10467i | ||||||||
\(944\) | −0.326003 | −0.0106105 | ||||||||
\(945\) | 11.6118 | + | 7.03813i | 0.377730 | + | 0.228950i | ||||
\(946\) | 8.13770 | 0.264579 | ||||||||
\(947\) | 21.5050i | 0.698819i | 0.936970 | + | 0.349409i | \(0.113618\pi\) | ||||
−0.936970 | + | 0.349409i | \(0.886382\pi\) | |||||||
\(948\) | − | 25.6192i | − | 0.832074i | ||||||
\(949\) | −1.67376 | −0.0543327 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 35.2928 | 1.14445 | ||||||||
\(952\) | 8.42663i | 0.273109i | ||||||||
\(953\) | 17.7301i | 0.574333i | 0.957881 | + | 0.287166i | \(0.0927133\pi\) | ||||
−0.957881 | + | 0.287166i | \(0.907287\pi\) | |||||||
\(954\) | 45.8865 | 1.48563 | ||||||||
\(955\) | 26.9622 | + | 16.3423i | 0.872475 | + | 0.528825i | ||||
\(956\) | −21.7290 | −0.702766 | ||||||||
\(957\) | − | 51.4417i | − | 1.66288i | ||||||
\(958\) | − | 31.7559i | − | 1.02599i | ||||||
\(959\) | −7.05960 | −0.227966 | ||||||||
\(960\) | −16.9045 | + | 27.8897i | −0.545591 | + | 0.900136i | ||||
\(961\) | 0.997355 | 0.0321727 | ||||||||
\(962\) | − | 0.160383i | − | 0.00517095i | ||||||
\(963\) | 6.85253i | 0.220820i | ||||||||
\(964\) | −6.01012 | −0.193573 | ||||||||
\(965\) | 4.60934 | − | 7.60465i | 0.148380 | − | 0.244802i | ||||
\(966\) | 5.08007 | 0.163448 | ||||||||
\(967\) | 13.6530i | 0.439052i | 0.975607 | + | 0.219526i | \(0.0704511\pi\) | ||||
−0.975607 | + | 0.219526i | \(0.929549\pi\) | |||||||
\(968\) | 20.6267i | 0.662966i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 25.0647 | + | 15.1922i | 0.804778 | + | 0.487793i | ||||
\(971\) | 27.9595 | 0.897263 | 0.448632 | − | 0.893717i | \(-0.351911\pi\) | ||||
0.448632 | + | 0.893717i | \(0.351911\pi\) | |||||||
\(972\) | 12.0544i | 0.386646i | ||||||||
\(973\) | − | 0.177457i | − | 0.00568901i | ||||||
\(974\) | 2.11791 | 0.0678622 | ||||||||
\(975\) | −1.38560 | − | 2.65514i | −0.0443749 | − | 0.0850326i | ||||
\(976\) | −0.308182 | −0.00986468 | ||||||||
\(977\) | − | 17.8540i | − | 0.571200i | −0.958349 | − | 0.285600i | \(-0.907807\pi\) | ||
0.958349 | − | 0.285600i | \(-0.0921929\pi\) | |||||||
\(978\) | 24.4082i | 0.780488i | ||||||||
\(979\) | 6.45094 | 0.206173 | ||||||||
\(980\) | −16.0365 | − | 9.72006i | −0.512267 | − | 0.310496i | ||||
\(981\) | −43.7109 | −1.39558 | ||||||||
\(982\) | − | 15.3526i | − | 0.489921i | ||||||
\(983\) | − | 49.0443i | − | 1.56427i | −0.623108 | − | 0.782136i | \(-0.714130\pi\) | ||
0.623108 | − | 0.782136i | \(-0.285870\pi\) | |||||||
\(984\) | 86.9210 | 2.77094 | ||||||||
\(985\) | −21.2677 | + | 35.0882i | −0.677645 | + | 1.11800i | ||||
\(986\) | −39.9166 | −1.27120 | ||||||||
\(987\) | − | 15.4194i | − | 0.490805i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 16.6489 | 0.529405 | ||||||||
\(990\) | −12.3933 | + | 20.4469i | −0.393885 | + | 0.649846i | ||||
\(991\) | −25.0673 | −0.796289 | −0.398145 | − | 0.917323i | \(-0.630346\pi\) | ||||
−0.398145 | + | 0.917323i | \(0.630346\pi\) | |||||||
\(992\) | − | 32.2059i | − | 1.02254i | ||||||
\(993\) | 18.0352i | 0.572331i | ||||||||
\(994\) | −2.53939 | −0.0805445 | ||||||||
\(995\) | −3.07236 | − | 1.86222i | −0.0974005 | − | 0.0590365i | ||||
\(996\) | 17.4650 | 0.553400 | ||||||||
\(997\) | − | 30.0222i | − | 0.950811i | −0.879767 | − | 0.475406i | \(-0.842301\pi\) | ||
0.879767 | − | 0.475406i | \(-0.157699\pi\) | |||||||
\(998\) | − | 25.2620i | − | 0.799656i | ||||||
\(999\) | −10.2426 | −0.324062 |
(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 | 1805.2.b.f.1084.2 | 6 | ||
5.2 | odd | 4 | 9025.2.a.bu.1.5 | 6 | |||
5.3 | odd | 4 | 9025.2.a.bu.1.2 | 6 | |||
5.4 | even | 2 | inner | 1805.2.b.f.1084.5 | 6 | ||
19.7 | even | 3 | 95.2.i.b.49.5 | yes | 12 | ||
19.11 | even | 3 | 95.2.i.b.64.2 | yes | 12 | ||
19.18 | odd | 2 | 1805.2.b.g.1084.5 | 6 | |||
57.11 | odd | 6 | 855.2.be.d.64.5 | 12 | |||
57.26 | odd | 6 | 855.2.be.d.334.2 | 12 | |||
95.7 | odd | 12 | 475.2.e.g.201.2 | 12 | |||
95.18 | even | 4 | 9025.2.a.bt.1.5 | 6 | |||
95.37 | even | 4 | 9025.2.a.bt.1.2 | 6 | |||
95.49 | even | 6 | 95.2.i.b.64.5 | yes | 12 | ||
95.64 | even | 6 | 95.2.i.b.49.2 | ✓ | 12 | ||
95.68 | odd | 12 | 475.2.e.g.26.5 | 12 | |||
95.83 | odd | 12 | 475.2.e.g.201.5 | 12 | |||
95.87 | odd | 12 | 475.2.e.g.26.2 | 12 | |||
95.94 | odd | 2 | 1805.2.b.g.1084.2 | 6 | |||
285.239 | odd | 6 | 855.2.be.d.64.2 | 12 | |||
285.254 | odd | 6 | 855.2.be.d.334.5 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
95.2.i.b.49.2 | ✓ | 12 | 95.64 | even | 6 | ||
95.2.i.b.49.5 | yes | 12 | 19.7 | even | 3 | ||
95.2.i.b.64.2 | yes | 12 | 19.11 | even | 3 | ||
95.2.i.b.64.5 | yes | 12 | 95.49 | even | 6 | ||
475.2.e.g.26.2 | 12 | 95.87 | odd | 12 | |||
475.2.e.g.26.5 | 12 | 95.68 | odd | 12 | |||
475.2.e.g.201.2 | 12 | 95.7 | odd | 12 | |||
475.2.e.g.201.5 | 12 | 95.83 | odd | 12 | |||
855.2.be.d.64.2 | 12 | 285.239 | odd | 6 | |||
855.2.be.d.64.5 | 12 | 57.11 | odd | 6 | |||
855.2.be.d.334.2 | 12 | 57.26 | odd | 6 | |||
855.2.be.d.334.5 | 12 | 285.254 | odd | 6 | |||
1805.2.b.f.1084.2 | 6 | 1.1 | even | 1 | trivial | ||
1805.2.b.f.1084.5 | 6 | 5.4 | even | 2 | inner | ||
1805.2.b.g.1084.2 | 6 | 95.94 | odd | 2 | |||
1805.2.b.g.1084.5 | 6 | 19.18 | odd | 2 | |||
9025.2.a.bt.1.2 | 6 | 95.37 | even | 4 | |||
9025.2.a.bt.1.5 | 6 | 95.18 | even | 4 | |||
9025.2.a.bu.1.2 | 6 | 5.3 | odd | 4 | |||
9025.2.a.bu.1.5 | 6 | 5.2 | odd | 4 |