Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [300,2,Mod(61,300)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(300, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 8]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("300.61");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 300.m (of order \(5\), degree \(4\), 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: | \(2.39551206064\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{5})\) |
Coefficient field: | 8.0.26265625.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} + 2x^{6} + x^{4} + 8x^{2} - 24x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 5 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 181.1 | ||
Root | \(1.33631 - 0.462894i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 300.181 |
Dual form | 300.2.m.b.121.1 |
$q$-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 \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(151\) | \(277\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{2}{5}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.809017 | − | 0.587785i | 0.467086 | − | 0.339358i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.57146 | + | 1.59076i | −0.702778 | + | 0.711409i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.32440 | 1.63447 | 0.817234 | − | 0.576306i | \(-0.195506\pi\) | ||||
0.817234 | + | 0.576306i | \(0.195506\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.309017 | − | 0.951057i | 0.103006 | − | 0.317019i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.180557 | + | 0.555698i | 0.0544401 | + | 0.167549i | 0.974580 | − | 0.224041i | \(-0.0719250\pi\) |
−0.920140 | + | 0.391590i | \(0.871925\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.298591 | − | 0.918969i | 0.0828143 | − | 0.254876i | −0.901073 | − | 0.433668i | \(-0.857219\pi\) |
0.983887 | + | 0.178792i | \(0.0572189\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.336312 | + | 2.21063i | −0.0868354 | + | 0.570783i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.88048 | + | 1.36625i | 0.456082 | + | 0.331363i | 0.791993 | − | 0.610531i | \(-0.209044\pi\) |
−0.335910 | + | 0.941894i | \(0.609044\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.35169 | + | 3.16169i | 0.998346 | + | 0.725341i | 0.961733 | − | 0.273988i | \(-0.0883430\pi\) |
0.0366134 | + | 0.999330i | \(0.488343\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.49851 | − | 2.54182i | 0.763437 | − | 0.554670i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.419687 | − | 1.29166i | −0.0875107 | − | 0.269330i | 0.897719 | − | 0.440569i | \(-0.145223\pi\) |
−0.985230 | + | 0.171238i | \(0.945223\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.0610333 | − | 4.99963i | −0.0122067 | − | 0.999925i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.309017 | − | 0.951057i | −0.0594703 | − | 0.183031i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.571459 | − | 0.415189i | 0.106117 | − | 0.0770987i | −0.533461 | − | 0.845825i | \(-0.679109\pi\) |
0.639578 | + | 0.768726i | \(0.279109\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.86707 | − | 4.98922i | −1.23336 | − | 0.896090i | −0.236225 | − | 0.971698i | \(-0.575910\pi\) |
−0.997138 | + | 0.0756084i | \(0.975910\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.472705 | + | 0.343440i | 0.0822874 | + | 0.0597853i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −6.79561 | + | 6.87908i | −1.14867 | + | 1.16278i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.89090 | + | 5.81960i | −0.310862 | + | 0.956736i | 0.666562 | + | 0.745450i | \(0.267765\pi\) |
−0.977424 | + | 0.211286i | \(0.932235\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.298591 | − | 0.918969i | −0.0478129 | − | 0.147153i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.41820 | − | 10.5201i | 0.533833 | − | 1.64297i | −0.212325 | − | 0.977199i | \(-0.568104\pi\) |
0.746158 | − | 0.665769i | \(-0.231896\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.03076 | −1.07218 | −0.536090 | − | 0.844161i | \(-0.680099\pi\) | ||||
−0.536090 | + | 0.844161i | \(0.680099\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.02729 | + | 1.98612i | 0.153140 | + | 0.296073i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7.33723 | + | 5.33081i | −1.07025 | + | 0.777579i | −0.975956 | − | 0.217966i | \(-0.930058\pi\) |
−0.0942890 | + | 0.995545i | \(0.530058\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 11.7004 | 1.67149 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.32440 | 0.325481 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.20487 | + | 5.23465i | −0.989665 | + | 0.719034i | −0.959848 | − | 0.280521i | \(-0.909493\pi\) |
−0.0298175 | + | 0.999555i | \(0.509493\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.16772 | − | 0.586034i | −0.157455 | − | 0.0790208i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.37899 | 0.712464 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.25351 | + | 6.93558i | −0.293382 | + | 0.902936i | 0.690379 | + | 0.723448i | \(0.257444\pi\) |
−0.983760 | + | 0.179487i | \(0.942556\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.48752 | − | 4.57810i | −0.190457 | − | 0.586166i | 0.809543 | − | 0.587061i | \(-0.199715\pi\) |
−1.00000 | 0.000895115i | \(0.999715\pi\) | ||||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.33631 | − | 4.11275i | 0.168359 | − | 0.518157i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.992636 | + | 1.91911i | 0.123121 | + | 0.238036i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.304195 | + | 0.221011i | 0.0371634 | + | 0.0270008i | 0.606212 | − | 0.795303i | \(-0.292688\pi\) |
−0.569049 | + | 0.822304i | \(0.692688\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.09875 | − | 0.798291i | −0.132274 | − | 0.0961030i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.54359 | + | 6.20729i | −1.01394 | + | 0.736669i | −0.965031 | − | 0.262134i | \(-0.915574\pi\) |
−0.0489067 | + | 0.998803i | \(0.515574\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.0659364 | + | 0.202931i | 0.00771727 | + | 0.0237513i | 0.954841 | − | 0.297117i | \(-0.0960252\pi\) |
−0.947124 | + | 0.320869i | \(0.896025\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.98808 | − | 4.00891i | −0.345034 | − | 0.462909i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.780801 | + | 2.40306i | 0.0889806 | + | 0.273854i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.68410 | − | 4.12974i | 0.639511 | − | 0.464632i | −0.220171 | − | 0.975461i | \(-0.570661\pi\) |
0.859682 | + | 0.510829i | \(0.170661\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.809017 | − | 0.587785i | −0.0898908 | − | 0.0653095i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −13.0343 | − | 9.46998i | −1.43070 | − | 1.03946i | −0.989886 | − | 0.141867i | \(-0.954690\pi\) |
−0.440815 | − | 0.897598i | \(-0.645310\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.12846 | + | 0.844386i | −0.556260 | + | 0.0915866i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.218278 | − | 0.671790i | 0.0234018 | − | 0.0720235i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.33233 | − | 13.3335i | −0.459226 | − | 1.41335i | −0.866101 | − | 0.499869i | \(-0.833382\pi\) |
0.406875 | − | 0.913484i | \(-0.366618\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.29123 | − | 3.97399i | 0.135357 | − | 0.416587i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −8.48817 | −0.880182 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −11.8680 | + | 1.95403i | −1.21763 | + | 0.200479i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −12.7436 | + | 9.25880i | −1.29392 | + | 0.940089i | −0.999877 | − | 0.0157030i | \(-0.995001\pi\) |
−0.294044 | + | 0.955792i | \(0.595001\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.584296 | 0.0587239 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.14178 | 0.710634 | 0.355317 | − | 0.934746i | \(-0.384373\pi\) | ||||
0.355317 | + | 0.934746i | \(0.384373\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.07238 | + | 0.779130i | −0.105665 | + | 0.0767699i | −0.639363 | − | 0.768905i | \(-0.720802\pi\) |
0.533698 | + | 0.845675i | \(0.320802\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.45435 | + | 9.55965i | −0.141930 | + | 0.932926i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 17.6796 | 1.70915 | 0.854573 | − | 0.519331i | \(-0.173819\pi\) | ||||
0.854573 | + | 0.519331i | \(0.173819\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.09385 | − | 3.36653i | 0.104772 | − | 0.322455i | −0.884905 | − | 0.465772i | \(-0.845777\pi\) |
0.989677 | + | 0.143317i | \(0.0457768\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.89090 | + | 5.81960i | 0.179476 | + | 0.552372i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.40414 | − | 16.6322i | 0.508379 | − | 1.56463i | −0.286636 | − | 0.958039i | \(-0.592537\pi\) |
0.795015 | − | 0.606590i | \(-0.207463\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.71425 | + | 1.36217i | 0.253105 | + | 0.127023i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.781722 | − | 0.567954i | −0.0722702 | − | 0.0525074i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 8.13192 | + | 5.90819i | 0.745452 | + | 0.541603i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.62299 | − | 6.26497i | 0.783908 | − | 0.569542i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.41820 | − | 10.5201i | −0.308208 | − | 0.948568i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 8.04912 | + | 7.75962i | 0.719935 | + | 0.694042i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.40966 | + | 16.6492i | 0.480030 | + | 1.47738i | 0.839052 | + | 0.544051i | \(0.183110\pi\) |
−0.359022 | + | 0.933329i | \(0.616890\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −5.68800 | + | 4.13258i | −0.500801 | + | 0.363853i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 15.2629 | + | 11.0892i | 1.33353 | + | 0.968865i | 0.999656 | + | 0.0262465i | \(0.00835549\pi\) |
0.333872 | + | 0.942618i | \(0.391645\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 18.8184 | + | 13.6724i | 1.63177 | + | 1.18555i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.99851 | + | 1.00297i | 0.172004 | + | 0.0863223i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.09472 | − | 12.6023i | 0.349836 | − | 1.07668i | −0.609108 | − | 0.793087i | \(-0.708472\pi\) |
0.958944 | − | 0.283596i | \(-0.0915275\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.22318 | − | 16.0753i | −0.443024 | − | 1.36349i | −0.884636 | − | 0.466283i | \(-0.845593\pi\) |
0.441611 | − | 0.897206i | \(-0.354407\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.80257 | + | 8.62543i | −0.236019 | + | 0.726393i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.564582 | 0.0472128 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.237558 | + | 1.56151i | −0.0197281 | + | 0.129676i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 9.46582 | − | 6.87732i | 0.780728 | − | 0.567232i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 12.1625 | 0.996388 | 0.498194 | − | 0.867066i | \(-0.333997\pi\) | ||||
0.498194 | + | 0.867066i | \(0.333997\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.84446 | −0.801131 | −0.400565 | − | 0.916268i | \(-0.631186\pi\) | ||||
−0.400565 | + | 0.916268i | \(0.631186\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.88048 | − | 1.36625i | 0.152027 | − | 0.110454i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 18.7280 | − | 3.08351i | 1.50427 | − | 0.247673i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −18.4804 | −1.47489 | −0.737447 | − | 0.675405i | \(-0.763969\pi\) | ||||
−0.737447 | + | 0.675405i | \(0.763969\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.75202 | + | 8.46984i | −0.218249 | + | 0.671702i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.81489 | − | 5.58566i | −0.143033 | − | 0.440212i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.49212 | + | 13.8253i | −0.351850 | + | 1.08288i | 0.605964 | + | 0.795492i | \(0.292788\pi\) |
−0.957814 | + | 0.287390i | \(0.907212\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.28917 | + | 0.212258i | −0.100362 | + | 0.0165242i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.63490 | + | 2.64091i | 0.281277 | + | 0.204360i | 0.719474 | − | 0.694519i | \(-0.244383\pi\) |
−0.438197 | + | 0.898879i | \(0.644383\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.76187 | + | 7.09242i | 0.750913 | + | 0.545570i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.35169 | − | 3.16169i | 0.332782 | − | 0.241780i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0.617465 | + | 1.90036i | 0.0469450 | + | 0.144482i | 0.971781 | − | 0.235883i | \(-0.0757983\pi\) |
−0.924836 | + | 0.380365i | \(0.875798\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.263932 | − | 21.6204i | −0.0199514 | − | 1.63435i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.25351 | + | 6.93558i | 0.169384 | + | 0.521310i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −11.3095 | + | 8.21683i | −0.845312 | + | 0.614155i | −0.923849 | − | 0.382756i | \(-0.874975\pi\) |
0.0785376 | + | 0.996911i | \(0.474975\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.9524 | − | 7.95740i | −0.814087 | − | 0.591469i | 0.100926 | − | 0.994894i | \(-0.467820\pi\) |
−0.915013 | + | 0.403425i | \(0.867820\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.89437 | − | 2.82942i | −0.287880 | − | 0.209157i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −6.28611 | − | 12.1532i | −0.462164 | − | 0.893523i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.419687 | + | 1.29166i | −0.0306905 | + | 0.0944557i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.33631 | − | 4.11275i | −0.0972024 | − | 0.299158i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.786594 | − | 2.42089i | 0.0569160 | − | 0.175169i | −0.918557 | − | 0.395288i | \(-0.870645\pi\) |
0.975473 | + | 0.220119i | \(0.0706446\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.60541 | 0.403486 | 0.201743 | − | 0.979438i | \(-0.435339\pi\) | ||||
0.201743 | + | 0.979438i | \(0.435339\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.93108 | + | 0.969136i | 0.138288 | + | 0.0694013i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.35580 | − | 4.61776i | 0.452832 | − | 0.329002i | −0.337881 | − | 0.941189i | \(-0.609710\pi\) |
0.790713 | + | 0.612187i | \(0.209710\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 16.9970 | 1.20489 | 0.602443 | − | 0.798162i | \(-0.294194\pi\) | ||||
0.602443 | + | 0.798162i | \(0.294194\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.376006 | 0.0265214 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.47122 | − | 1.79544i | 0.173445 | − | 0.126015i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 11.3634 | + | 21.9695i | 0.793657 | + | 1.53441i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.35813 | −0.0943969 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.971215 | + | 2.98909i | −0.0671804 | + | 0.206760i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.00341 | − | 12.3212i | −0.275606 | − | 0.848229i | −0.989058 | − | 0.147525i | \(-0.952869\pi\) |
0.713452 | − | 0.700704i | \(-0.247131\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3.26336 | + | 10.0436i | −0.223602 | + | 0.688176i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 11.0485 | − | 11.1842i | 0.753505 | − | 0.762759i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −29.6959 | − | 21.5754i | −2.01589 | − | 1.46463i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.172624 | + | 0.125419i | 0.0116648 | + | 0.00847500i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.81703 | − | 1.32015i | 0.122227 | − | 0.0888030i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.86518 | + | 18.0512i | 0.392761 | + | 1.20880i | 0.930691 | + | 0.365806i | \(0.119207\pi\) |
−0.537930 | + | 0.842990i | \(0.680793\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.77379 | − | 1.48692i | −0.318253 | − | 0.0991283i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −0.119005 | − | 0.366260i | −0.00789865 | − | 0.0243095i | 0.947030 | − | 0.321147i | \(-0.104068\pi\) |
−0.954928 | + | 0.296837i | \(0.904068\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.30740 | + | 6.03568i | −0.548968 | + | 0.398849i | −0.827405 | − | 0.561606i | \(-0.810184\pi\) |
0.278437 | + | 0.960455i | \(0.410184\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.04416 | + | 1.48517i | 0.134496 | + | 0.0977172i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 17.5055 | + | 12.7185i | 1.14682 | + | 0.833217i | 0.988055 | − | 0.154099i | \(-0.0492474\pi\) |
0.158769 | + | 0.987316i | \(0.449247\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.05012 | − | 20.0489i | 0.198968 | − | 1.30785i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.17113 | − | 6.68206i | 0.141030 | − | 0.434047i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.38438 | − | 7.33836i | −0.154233 | − | 0.474679i | 0.843850 | − | 0.536579i | \(-0.180284\pi\) |
−0.998082 | + | 0.0619006i | \(0.980284\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.82629 | + | 24.0868i | −0.504136 | + | 1.55157i | 0.298083 | + | 0.954540i | \(0.403653\pi\) |
−0.802219 | + | 0.597030i | \(0.796347\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −18.3867 | + | 18.6125i | −1.17468 | + | 1.18911i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.20487 | − | 3.05502i | 0.267550 | − | 0.194386i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −16.1113 | −1.02101 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.39913 | −0.151432 | −0.0757160 | − | 0.997129i | \(-0.524124\pi\) | ||||
−0.0757160 | + | 0.997129i | \(0.524124\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.641997 | − | 0.466438i | 0.0403620 | − | 0.0293247i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3.65269 | + | 3.69756i | −0.228741 | + | 0.231550i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −14.3086 | −0.892548 | −0.446274 | − | 0.894896i | \(-0.647249\pi\) | ||||
−0.446274 | + | 0.894896i | \(0.647249\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8.17701 | + | 25.1662i | −0.508095 | + | 1.56375i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.218278 | − | 0.671790i | −0.0135111 | − | 0.0415828i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.04210 | − | 12.4403i | 0.249247 | − | 0.767103i | −0.745662 | − | 0.666324i | \(-0.767867\pi\) |
0.994909 | − | 0.100779i | \(-0.0321334\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.99510 | − | 19.6873i | 0.183987 | − | 1.20938i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −11.3422 | − | 8.24058i | −0.694131 | − | 0.504315i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −24.8165 | − | 18.0302i | −1.51309 | − | 1.09932i | −0.964783 | − | 0.263046i | \(-0.915273\pi\) |
−0.548306 | − | 0.836278i | \(-0.684727\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −11.5174 | + | 8.36785i | −0.699629 | + | 0.508310i | −0.879811 | − | 0.475323i | \(-0.842331\pi\) |
0.180182 | + | 0.983633i | \(0.442331\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.29123 | − | 3.97399i | −0.0781486 | − | 0.240517i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.76726 | − | 0.936635i | 0.166872 | − | 0.0564812i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.22072 | + | 19.1454i | 0.373767 | + | 1.15034i | 0.944307 | + | 0.329066i | \(0.106734\pi\) |
−0.570540 | + | 0.821270i | \(0.693266\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −6.86707 | + | 4.98922i | −0.411121 | + | 0.298697i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.94172 | + | 5.77000i | 0.473763 | + | 0.344209i | 0.798906 | − | 0.601456i | \(-0.205412\pi\) |
−0.325143 | + | 0.945665i | \(0.605412\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.29540 | − | 3.84733i | −0.314779 | − | 0.228700i | 0.419166 | − | 0.907910i | \(-0.362323\pi\) |
−0.733944 | + | 0.679210i | \(0.762323\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −8.45286 | + | 8.55667i | −0.500704 | + | 0.506854i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 14.7816 | − | 45.4932i | 0.872532 | − | 2.68538i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.58373 | − | 11.0296i | −0.210807 | − | 0.648799i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.86764 | + | 14.9811i | −0.285346 | + | 0.878205i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0.869428 | 0.0507925 | 0.0253963 | − | 0.999677i | \(-0.491915\pi\) | ||||
0.0253963 | + | 0.999677i | \(0.491915\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.49155 | − | 14.4838i | −0.436175 | − | 0.843277i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.472705 | − | 0.343440i | 0.0274291 | − | 0.0199284i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.31231 | −0.0758930 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −30.4038 | −1.75244 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 5.77782 | − | 4.19783i | 0.331927 | − | 0.241159i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 9.62023 | + | 4.82802i | 0.550853 | + | 0.276452i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 21.7261 | 1.23997 | 0.619986 | − | 0.784613i | \(-0.287138\pi\) | ||||
0.619986 | + | 0.784613i | \(0.287138\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.409613 | + | 1.26066i | −0.0233021 | + | 0.0717163i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.86610 | + | 18.0540i | 0.332636 | + | 1.02375i | 0.967875 | + | 0.251432i | \(0.0809016\pi\) |
−0.635239 | + | 0.772316i | \(0.719098\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.87947 | + | 5.78443i | −0.106234 | + | 0.326955i | −0.990018 | − | 0.140940i | \(-0.954988\pi\) |
0.883784 | + | 0.467895i | \(0.154988\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 4.44243 | + | 8.58876i | 0.250303 | + | 0.483922i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.60038 | − | 1.16274i | −0.0898860 | − | 0.0653060i | 0.541935 | − | 0.840421i | \(-0.317692\pi\) |
−0.631821 | + | 0.775115i | \(0.717692\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.333901 | + | 0.242593i | 0.0186949 | + | 0.0135826i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 14.3031 | − | 10.3918i | 0.798319 | − | 0.580013i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.86361 | + | 11.8910i | 0.214977 | + | 0.661631i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.61273 | − | 1.43676i | −0.255868 | − | 0.0796970i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.09385 | − | 3.36653i | −0.0604901 | − | 0.186169i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −31.7291 | + | 23.0525i | −1.74928 | + | 1.27093i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.6230 | + | 7.71805i | 0.583892 | + | 0.424223i | 0.840125 | − | 0.542393i | \(-0.182481\pi\) |
−0.256233 | + | 0.966615i | \(0.582481\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.95044 | + | 3.59671i | 0.271283 | + | 0.197098i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.829605 | + | 0.136592i | −0.0453262 | + | 0.00746283i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.55245 | − | 10.9333i | 0.193514 | − | 0.595576i | −0.806476 | − | 0.591266i | \(-0.798628\pi\) |
0.999991 | − | 0.00430942i | \(-0.00137173\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5.40414 | − | 16.6322i | −0.293513 | − | 0.903339i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.53260 | − | 4.71686i | 0.0829949 | − | 0.255432i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.3264 | 1.09752 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.99654 | − | 0.493371i | 0.161328 | − | 0.0265622i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −24.0905 | + | 17.5028i | −1.29325 | + | 0.939599i | −0.999866 | − | 0.0163966i | \(-0.994781\pi\) |
−0.293381 | + | 0.955995i | \(0.594781\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10.0870 | 0.539946 | 0.269973 | − | 0.962868i | \(-0.412985\pi\) | ||||
0.269973 | + | 0.962868i | \(0.412985\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.966262 | −0.0515752 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 11.5382 | − | 8.38300i | 0.614117 | − | 0.446182i | −0.236745 | − | 0.971572i | \(-0.576081\pi\) |
0.850862 | + | 0.525390i | \(0.176081\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.55161 | − | 23.3453i | 0.188500 | − | 1.23904i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 10.0516 | 0.531988 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2.04232 | + | 6.28562i | −0.107790 | + | 0.331742i | −0.990375 | − | 0.138410i | \(-0.955801\pi\) |
0.882585 | + | 0.470152i | \(0.155801\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.06962 | + | 9.44731i | 0.161559 | + | 0.497227i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.29369 | − | 10.1369i | 0.172874 | − | 0.532051i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.426432 | − | 0.214009i | −0.0223204 | − | 0.0112018i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −7.72012 | − | 5.60900i | −0.402987 | − | 0.292787i | 0.367770 | − | 0.929917i | \(-0.380122\pi\) |
−0.770757 | + | 0.637130i | \(0.780122\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −8.94895 | − | 6.50180i | −0.465864 | − | 0.338470i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −31.1567 | + | 22.6367i | −1.61758 | + | 1.17524i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −0.402767 | − | 1.23959i | −0.0208545 | − | 0.0641835i | 0.940088 | − | 0.340933i | \(-0.110743\pi\) |
−0.960942 | + | 0.276749i | \(0.910743\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 11.0729 | + | 1.54651i | 0.571800 | + | 0.0798615i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −0.210914 | − | 0.649125i | −0.0108626 | − | 0.0334317i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −19.6474 | + | 14.2747i | −1.00922 | + | 0.733240i | −0.964045 | − | 0.265739i | \(-0.914384\pi\) |
−0.0451733 | + | 0.998979i | \(0.514384\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 14.1627 | + | 10.2898i | 0.725576 | + | 0.527162i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −9.81489 | − | 7.13094i | −0.501518 | − | 0.364374i | 0.308079 | − | 0.951361i | \(-0.400314\pi\) |
−0.809596 | + | 0.586987i | \(0.800314\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5.04969 | − | 2.53424i | −0.257356 | − | 0.129157i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.17262 | + | 6.68665i | −0.110441 | + | 0.339901i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −9.04178 | − | 27.8278i | −0.458437 | − | 1.41092i | −0.867053 | − | 0.498217i | \(-0.833988\pi\) |
0.408616 | − | 0.912706i | \(-0.366012\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.975518 | − | 3.00234i | 0.0493341 | − | 0.151835i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 18.8660 | 0.951664 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.36291 | + | 15.5318i | −0.118891 | + | 0.781488i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.09179 | + | 3.69940i | −0.255550 | + | 0.185668i | −0.708183 | − | 0.706029i | \(-0.750485\pi\) |
0.452633 | + | 0.891697i | \(0.350485\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 23.2609 | 1.16450 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 30.3064 | 1.51343 | 0.756714 | − | 0.653747i | \(-0.226804\pi\) | ||||
0.756714 | + | 0.653747i | \(0.226804\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.63539 | + | 4.82089i | −0.330532 | + | 0.240146i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.20636 | − | 0.363271i | 0.109635 | − | 0.0180511i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.57536 | −0.177224 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.70942 | − | 17.5718i | 0.282313 | − | 0.868870i | −0.704878 | − | 0.709328i | \(-0.748998\pi\) |
0.987191 | − | 0.159541i | \(-0.0510015\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.09472 | − | 12.6023i | −0.201978 | − | 0.621623i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −9.74505 | + | 29.9922i | −0.479523 | + | 1.47582i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 35.5473 | − | 5.85277i | 1.74495 | − | 0.287301i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −13.6745 | − | 9.93508i | −0.669641 | − | 0.486523i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 18.1586 | + | 13.1930i | 0.887108 | + | 0.644522i | 0.935122 | − | 0.354325i | \(-0.115289\pi\) |
−0.0480143 | + | 0.998847i | \(0.515289\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.05679 | − | 3.67397i | 0.246453 | − | 0.179058i | −0.457700 | − | 0.889106i | \(-0.651327\pi\) |
0.704153 | + | 0.710048i | \(0.251327\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.80257 | + | 8.62543i | 0.136266 | + | 0.419383i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6.71595 | − | 9.48507i | 0.325771 | − | 0.460093i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.43260 | − | 19.7975i | −0.311296 | − | 0.958069i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.456757 | − | 0.331853i | 0.0220524 | − | 0.0160220i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −27.9850 | − | 20.3323i | −1.34799 | − | 0.979373i | −0.999109 | − | 0.0422061i | \(-0.986561\pi\) |
−0.348882 | − | 0.937167i | \(-0.613439\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.18056 | + | 2.31081i | 0.152848 | + | 0.111050i | 0.661581 | − | 0.749874i | \(-0.269886\pi\) |
−0.508733 | + | 0.860924i | \(0.669886\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.725642 | + | 1.40292i | 0.0347919 | + | 0.0672648i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.25749 | − | 6.94784i | 0.107990 | − | 0.332360i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.54170 | + | 4.74487i | 0.0735815 | + | 0.226460i | 0.981083 | − | 0.193589i | \(-0.0620128\pi\) |
−0.907501 | + | 0.420049i | \(0.862013\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.61562 | − | 11.1277i | 0.172173 | − | 0.529893i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 9.92754 | 0.471672 | 0.235836 | − | 0.971793i | \(-0.424217\pi\) | ||||
0.235836 | + | 0.971793i | \(0.424217\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 28.0185 | + | 14.0614i | 1.32821 | + | 0.666575i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 9.83964 | − | 7.14892i | 0.465399 | − | 0.338132i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9.87365 | 0.465966 | 0.232983 | − | 0.972481i | \(-0.425151\pi\) | ||||
0.232983 | + | 0.972481i | \(0.425151\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.46320 | 0.304340 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −7.96433 | + | 5.78643i | −0.374197 | + | 0.271870i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4.29255 | + | 8.29899i | 0.201238 | + | 0.389063i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 12.6424 | 0.591387 | 0.295693 | − | 0.955283i | \(-0.404449\pi\) | ||||
0.295693 | + | 0.955283i | \(0.404449\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.718278 | − | 2.21063i | 0.0335263 | − | 0.103183i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12.2911 | + | 37.8280i | 0.572452 | + | 1.76183i | 0.644697 | + | 0.764438i | \(0.276984\pi\) |
−0.0722451 | + | 0.997387i | \(0.523016\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.36545 | − | 4.20242i | 0.0634578 | − | 0.195303i | −0.914301 | − | 0.405035i | \(-0.867259\pi\) |
0.977759 | + | 0.209732i | \(0.0672592\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 13.3388 | − | 13.5026i | 0.618572 | − | 0.626170i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 9.12137 | + | 6.62706i | 0.422086 | + | 0.306664i | 0.778477 | − | 0.627673i | \(-0.215993\pi\) |
−0.356390 | + | 0.934337i | \(0.615993\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.31546 | + | 0.955738i | 0.0607423 | + | 0.0441319i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −14.9509 | + | 10.8625i | −0.688902 | + | 0.500517i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.26945 | − | 3.90698i | −0.0583696 | − | 0.179643i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 15.5417 | − | 21.9498i | 0.713101 | − | 1.00713i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.75202 | + | 8.46984i | 0.126006 | + | 0.387807i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4.49728 | − | 3.26747i | 0.205486 | − | 0.149294i | −0.480283 | − | 0.877114i | \(-0.659466\pi\) |
0.685769 | + | 0.727819i | \(0.259466\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.78343 | + | 3.47536i | 0.218105 | + | 0.158463i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −4.75145 | − | 3.45213i | −0.216198 | − | 0.157077i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 5.29759 | − | 34.8219i | 0.240551 | − | 1.58118i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5.14021 | + | 15.8199i | −0.232925 | + | 0.716870i | 0.764465 | + | 0.644665i | \(0.223003\pi\) |
−0.997390 | + | 0.0722042i | \(0.976997\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4.49212 | + | 13.8253i | 0.203141 | + | 0.625202i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.327326 | − | 1.00741i | 0.0147720 | − | 0.0454636i | −0.943399 | − | 0.331661i | \(-0.892391\pi\) |
0.958171 | + | 0.286197i | \(0.0923912\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.64187 | 0.0739459 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.918197 | + | 0.929474i | −0.0412699 | + | 0.0417767i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −36.9459 | + | 26.8428i | −1.65725 | + | 1.20406i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 24.9700 | 1.11781 | 0.558906 | − | 0.829231i | \(-0.311221\pi\) | ||||
0.558906 | + | 0.829231i | \(0.311221\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4.49299 | 0.200732 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −10.1502 | + | 7.37458i | −0.452576 | + | 0.328816i | −0.790612 | − | 0.612317i | \(-0.790238\pi\) |
0.338036 | + | 0.941133i | \(0.390238\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −11.2230 | + | 11.3609i | −0.499418 | + | 0.505551i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 12.0663 | 0.535885 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4.76735 | + | 14.6724i | −0.211309 | + | 0.650342i | 0.788086 | + | 0.615565i | \(0.211072\pi\) |
−0.999395 | + | 0.0347770i | \(0.988928\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.285135 | + | 0.877556i | 0.0126136 | + | 0.0388208i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.66220 | − | 5.11572i | 0.0733878 | − | 0.225865i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.445793 | − | 2.93027i | 0.0196440 | − | 0.129123i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.28711 | − | 3.11477i | −0.188547 | − | 0.136987i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.61654 | + | 1.17449i | 0.0709584 | + | 0.0515543i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 15.6466 | − | 11.3679i | 0.685490 | − | 0.498037i | −0.189685 | − | 0.981845i | \(-0.560747\pi\) |
0.875174 | + | 0.483808i | \(0.160747\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.14779 | + | 6.61022i | 0.0939163 | + | 0.289045i | 0.986970 | − | 0.160906i | \(-0.0514416\pi\) |
−0.893053 | + | 0.449951i | \(0.851442\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −12.9217 | − | 17.3361i | −0.563947 | − | 0.756610i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −6.09686 | − | 18.7642i | −0.265583 | − | 0.817382i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 17.1151 | − | 12.4349i | 0.744136 | − | 0.540647i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5.89976 | + | 4.28642i | 0.256028 | + | 0.186015i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −8.64703 | − | 6.28244i | −0.374545 | − | 0.272123i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −27.7827 | + | 28.1239i | −1.20115 | + | 1.21590i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −4.31984 | + | 13.2951i | −0.186415 | + | 0.573727i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.11259 | + | 6.50189i | 0.0909958 | + | 0.280056i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.75145 | − | 5.39040i | 0.0753006 | − | 0.231751i | −0.906321 | − | 0.422590i | \(-0.861121\pi\) |
0.981621 | + | 0.190839i | \(0.0611209\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −13.5379 | −0.580968 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.63639 | + | 7.03041i | 0.155766 | + | 0.301150i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −10.0315 | + | 7.28835i | −0.428918 | + | 0.311627i | −0.781216 | − | 0.624261i | \(-0.785400\pi\) |
0.352298 | + | 0.935888i | \(0.385400\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −4.81370 | −0.205444 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.79951 | 0.161865 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 24.5803 | − | 17.8586i | 1.04526 | − | 0.759427i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −12.2291 | − | 6.13729i | −0.519094 | − | 0.260513i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 24.8970 | 1.05492 | 0.527461 | − | 0.849579i | \(-0.323144\pi\) | ||||
0.527461 | + | 0.849579i | \(0.323144\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.09932 | + | 6.46105i | −0.0887919 | + | 0.273273i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.419687 | + | 1.29166i | 0.0177192 | + | 0.0545340i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −7.73423 | + | 23.8035i | −0.325959 | + | 1.00320i | 0.645047 | + | 0.764143i | \(0.276838\pi\) |
−0.971006 | + | 0.239055i | \(0.923162\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 17.9655 | + | 34.7336i | 0.755814 | + | 1.46125i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −3.49851 | − | 2.54182i | −0.146924 | − | 0.106746i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.69282 | − | 1.22991i | −0.0709669 | − | 0.0515605i | 0.551736 | − | 0.834019i | \(-0.313966\pi\) |
−0.622703 | + | 0.782458i | \(0.713966\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.32956 | − | 6.77832i | 0.390430 | − | 0.283664i | −0.375202 | − | 0.926943i | \(-0.622427\pi\) |
0.765632 | + | 0.643279i | \(0.222427\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −0.786594 | − | 2.42089i | −0.0328604 | − | 0.101134i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −6.43222 | + | 2.17711i | −0.268242 | + | 0.0907918i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.80625 | − | 5.55908i | −0.0751954 | − | 0.231427i | 0.906393 | − | 0.422435i | \(-0.138825\pi\) |
−0.981589 | + | 0.191007i | \(0.938825\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4.53487 | − | 3.29478i | 0.188463 | − | 0.136926i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −56.3655 | − | 40.9519i | −2.33843 | − | 1.69897i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.20978 | − | 3.05858i | −0.174351 | − | 0.126673i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.13192 | − | 0.351015i | 0.0881442 | − | 0.0145127i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −2.84381 | + | 8.75234i | −0.117377 | + | 0.361248i | −0.992435 | − | 0.122769i | \(-0.960823\pi\) |
0.875059 | + | 0.484017i | \(0.160823\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −14.1090 | − | 43.4231i | −0.581352 | − | 1.78922i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.42770 | − | 7.47170i | 0.0998623 | − | 0.307345i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −14.9033 | −0.612004 | −0.306002 | − | 0.952031i | \(-0.598991\pi\) | ||||
−0.306002 | + | 0.952031i | \(0.598991\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −22.1775 | + | 3.65146i | −0.909189 | + | 0.149695i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 13.7509 | − | 9.99060i | 0.562786 | − | 0.408888i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7.52244 | −0.307359 | −0.153679 | − | 0.988121i | \(-0.549112\pi\) | ||||
−0.153679 | + | 0.988121i | \(0.549112\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18.6618 | 0.761232 | 0.380616 | − | 0.924733i | \(-0.375712\pi\) | ||||
0.380616 | + | 0.924733i | \(0.375712\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.304195 | − | 0.221011i | 0.0123878 | − | 0.00900025i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.58461 | + | 23.5622i | −0.145735 | + | 0.957941i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0.810016 | 0.0328776 | 0.0164388 | − | 0.999865i | \(-0.494767\pi\) | ||||
0.0164388 | + | 0.999865i | \(0.494767\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.943920 | − | 2.90509i | 0.0382496 | − | 0.117720i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.70802 | + | 8.33443i | 0.109555 | + | 0.337175i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.54232 | − | 4.74678i | 0.0622938 | − | 0.191721i | −0.915066 | − | 0.403304i | \(-0.867862\pi\) |
0.977360 | + | 0.211583i | \(0.0678619\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 22.1066 | + | 11.0944i | 0.891422 | + | 0.447370i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 34.4722 | + | 25.0455i | 1.38780 | + | 1.00829i | 0.996103 | + | 0.0881990i | \(0.0281111\pi\) |
0.391695 | + | 0.920095i | \(0.371889\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −29.9038 | − | 21.7264i | −1.20193 | − | 0.873257i | −0.207461 | − | 0.978243i | \(-0.566520\pi\) |
−0.994474 | + | 0.104987i | \(0.966520\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.09875 | + | 0.798291i | −0.0440915 | + | 0.0320343i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −18.7347 | − | 57.6595i | −0.750590 | − | 2.31008i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −24.9925 | + | 0.610287i | −0.999702 | + | 0.0244115i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.971215 | + | 2.98909i | 0.0387866 | + | 0.119373i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −11.5068 | + | 8.36018i | −0.458806 | + | 0.333342i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 26.8891 | + | 19.5361i | 1.07044 | + | 0.777719i | 0.975991 | − | 0.217811i | \(-0.0698915\pi\) |
0.0944476 | + | 0.995530i | \(0.469892\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −10.4811 | − | 7.61494i | −0.416585 | − | 0.302667i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −34.9860 | − | 17.5581i | −1.38838 | − | 0.696772i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.49364 | − | 10.7523i | 0.138423 | − | 0.426022i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.26336 | + | 10.0436i | 0.129097 | + | 0.397319i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −8.41649 | + | 25.9033i | −0.332431 | + | 1.02312i | 0.635542 | + | 0.772066i | \(0.280777\pi\) |
−0.967974 | + | 0.251052i | \(0.919223\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −12.8557 | −0.506978 | −0.253489 | − | 0.967338i | \(-0.581578\pi\) | ||||
−0.253489 | + | 0.967338i | \(0.581578\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.36453 | − | 15.5424i | 0.0931032 | − | 0.611982i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −25.7597 | + | 18.7155i | −1.01272 | + | 0.735784i | −0.964778 | − | 0.263066i | \(-0.915266\pi\) |
−0.0479418 | + | 0.998850i | \(0.515266\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.26098 | −0.167258 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −36.7062 | −1.43863 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 11.7323 | − | 8.52402i | 0.459121 | − | 0.333571i | −0.334066 | − | 0.942550i | \(-0.608421\pi\) |
0.793186 | + | 0.608979i | \(0.208421\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −41.6253 | + | 6.85348i | −1.62643 | + | 0.267788i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0.213375 | 0.00832454 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 10.2713 | − | 31.6118i | 0.400113 | − | 1.23142i | −0.524795 | − | 0.851229i | \(-0.675858\pi\) |
0.924908 | − | 0.380192i | \(-0.124142\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9.84316 | − | 30.2941i | −0.382854 | − | 1.17830i | −0.938025 | − | 0.346568i | \(-0.887347\pi\) |
0.555170 | − | 0.831737i | \(-0.312653\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.694044 | − | 2.13605i | 0.0269545 | − | 0.0829573i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −51.3219 | + | 8.45000i | −1.99018 | + | 0.327677i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.776118 | − | 0.563883i | −0.0300514 | − | 0.0218336i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 15.3552 | + | 11.1562i | 0.593668 | + | 0.431325i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.27546 | − | 1.65322i | 0.0878432 | − | 0.0638218i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8.09358 | − | 24.9095i | −0.311985 | − | 0.960190i | −0.976978 | − | 0.213341i | \(-0.931566\pi\) |
0.664993 | − | 0.746849i | \(-0.268434\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.73607 | + | 1.60302i | −0.182291 | + | 0.0617001i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −4.58711 | − | 14.1177i | −0.176297 | − | 0.542586i | 0.823393 | − | 0.567471i | \(-0.192078\pi\) |
−0.999690 | + | 0.0248849i | \(0.992078\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −55.1086 | + | 40.0387i | −2.11487 | + | 1.53655i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.311560 | − | 0.226361i | −0.0119390 | − | 0.00867418i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 4.55174 | + | 3.30703i | 0.174168 | + | 0.126540i | 0.671454 | − | 0.741046i | \(-0.265670\pi\) |
−0.497286 | + | 0.867586i | \(0.665670\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 13.6125 | + | 26.3176i | 0.520106 | + | 1.00555i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3.17314 | + | 9.76593i | −0.121063 | + | 0.372593i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.65917 | + | 8.18408i | 0.101306 | + | 0.311788i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 10.6330 | − | 32.7249i | 0.404497 | − | 1.24492i | −0.516817 | − | 0.856096i | \(-0.672883\pi\) |
0.921314 | − | 0.388819i | \(-0.127117\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.52673 | 0.0959824 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 33.7800 | + | 16.9528i | 1.28135 | + | 0.643058i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 20.8009 | − | 15.1128i | 0.787891 | − | 0.572436i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 21.6380 | 0.818425 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8.86294 | 0.334749 | 0.167374 | − | 0.985893i | \(-0.446471\pi\) | ||||
0.167374 | + | 0.985893i | \(0.446471\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −26.6284 | + | 19.3466i | −1.00431 | + | 0.729673i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −9.31686 | − | 18.0127i | −0.350893 | − | 0.678399i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 30.8839 | 1.16151 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0.474877 | − | 1.46152i | 0.0178344 | − | 0.0548885i | −0.941743 | − | 0.336333i | \(-0.890813\pi\) |
0.959578 | + | 0.281444i | \(0.0908134\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.17113 | − | 6.68206i | −0.0814239 | − | 0.250597i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −3.56237 | + | 10.9638i | −0.133412 | + | 0.410599i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.887218 | + | 0.898115i | −0.0331801 | + | 0.0335876i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −6.24238 | − | 4.53535i | −0.233126 | − | 0.169376i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 15.4808 | + | 11.2474i | 0.577335 | + | 0.419459i | 0.837762 | − | 0.546035i | \(-0.183863\pi\) |
−0.260427 | + | 0.965493i | \(0.583863\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.63740 | + | 3.36926i | −0.172706 | + | 0.125478i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 7.82629 | + | 24.0868i | 0.291063 | + | 0.895799i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.11067 | − | 2.83174i | −0.0783883 | − | 0.105168i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 14.4649 | + | 44.5184i | 0.536474 | + | 1.65110i | 0.740443 | + | 0.672119i | \(0.234616\pi\) |
−0.203970 | + | 0.978977i | \(0.565384\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −0.809017 | + | 0.587785i | −0.0299636 | + | 0.0217698i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −13.2212 | − | 9.60574i | −0.489003 | − | 0.355281i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −41.2634 | − | 29.9796i | −1.52410 | − | 1.10732i | −0.959409 | − | 0.282019i | \(-0.908996\pi\) |
−0.564690 | − | 0.825303i | \(-0.691004\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −3.93498 | + | 25.8653i | −0.145144 | + | 0.954055i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −0.0678906 | + | 0.208946i | −0.00250078 | + | 0.00769662i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.08075 | + | 12.5592i | 0.150113 | + | 0.461999i | 0.997633 | − | 0.0687637i | \(-0.0219054\pi\) |
−0.847520 | + | 0.530763i | \(0.821905\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.60612 | − | 4.94312i | 0.0590022 | − | 0.181590i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 10.6063 | 0.389107 | 0.194553 | − | 0.980892i | \(-0.437674\pi\) | ||||
0.194553 | + | 0.980892i | \(0.437674\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −19.1128 | + | 19.3476i | −0.700240 | + | 0.708840i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −13.0343 | + | 9.46998i | −0.476900 | + | 0.346488i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 76.4534 | 2.79355 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 28.2581 | 1.03115 | 0.515577 | − | 0.856843i | \(-0.327578\pi\) | ||||
0.515577 | + | 0.856843i | \(0.327578\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.94094 | + | 1.41018i | −0.0707318 | + | 0.0513897i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 15.4702 | − | 15.6602i | 0.563017 | − | 0.569932i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 27.7474 | 1.00849 | 0.504247 | − | 0.863559i | \(-0.331770\pi\) | ||||
0.504247 | + | 0.863559i | \(0.331770\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.245221 | − | 0.754713i | 0.00890096 | − | 0.0273943i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4.97988 | − | 15.3265i | −0.180521 | − | 0.555585i | 0.819322 | − | 0.573334i | \(-0.194350\pi\) |
−0.999842 | + | 0.0177487i | \(0.994350\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.73024 | − | 14.5582i | 0.171246 | − | 0.527042i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.781722 | + | 5.13838i | −0.0282632 | + | 0.185779i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 5.70071 | + | 4.14181i | 0.205841 | + | 0.149552i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 28.1081 | + | 20.4217i | 1.01360 | + | 0.736426i | 0.964962 | − | 0.262390i | \(-0.0845108\pi\) |
0.0486417 | + | 0.998816i | \(0.484511\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −11.5759 | + | 8.41040i | −0.416897 | + | 0.302893i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 7.25215 | + | 22.3198i | 0.260842 | + | 0.802788i | 0.992622 | + | 0.121248i | \(0.0386896\pi\) |
−0.731781 | + | 0.681540i | \(0.761310\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −24.5251 | + | 34.6373i | −0.880968 | + | 1.24421i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 8.17701 | + | 25.1662i | 0.293349 | + | 0.902834i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 48.1363 | − | 34.9731i | 1.72466 | − | 1.25304i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.99199 | − | 3.62689i | −0.178627 | − | 0.129780i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −0.571459 | − | 0.415189i | −0.0204223 | − | 0.0148377i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 29.0411 | − | 29.3978i | 1.03652 | − | 1.04925i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −7.91755 | + | 24.3677i | −0.282230 | + | 0.868615i | 0.704985 | + | 0.709222i | \(0.250954\pi\) |
−0.987215 | + | 0.159393i | \(0.949046\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −4.04210 | − | 12.4403i | −0.143903 | − | 0.442887i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 23.3696 | − | 71.9244i | 0.830929 | − | 2.55734i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.65129 | −0.165172 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −9.14879 | − | 17.6878i | −0.324474 | − | 0.627321i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.55577 | − | 1.13034i | 0.0551083 | − | 0.0400386i | −0.559890 | − | 0.828567i | \(-0.689157\pi\) |
0.614998 | + | 0.788528i | \(0.289157\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −21.0807 | −0.745781 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −14.0197 | −0.495362 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.100863 | + | 0.0732815i | −0.00355939 | + | 0.00258605i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 11.7375 | + | 5.89058i | 0.413692 | + | 0.207616i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −30.6749 | −1.07981 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −14.0321 | + | 43.1862i | −0.493341 | + | 1.51835i | 0.326185 | + | 0.945306i | \(0.394237\pi\) |
−0.819526 | + | 0.573041i | \(0.805763\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −7.39190 | − | 22.7499i | −0.259565 | − | 0.798858i | −0.992896 | − | 0.118987i | \(-0.962035\pi\) |
0.733331 | − | 0.679872i | \(-0.237965\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4.39924 | + | 13.5395i | −0.154288 | + | 0.474850i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −14.9336 | − | 28.8718i | −0.523100 | − | 1.01133i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −30.5957 | − | 22.2291i | −1.07041 | − | 0.777697i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.38048 | − | 2.45606i | −0.118123 | − | 0.0858217i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 25.5538 | − | 18.5659i | 0.891834 | − | 0.647955i | −0.0445216 | − | 0.999008i | \(-0.514176\pi\) |
0.936356 | + | 0.351053i | \(0.114176\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.63669 | + | 8.11491i | 0.0919094 | + | 0.282868i | 0.986436 | − | 0.164147i | \(-0.0524871\pi\) |
−0.894527 | + | 0.447015i | \(0.852487\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.68822 | − | 2.38431i | 0.0587764 | − | 0.0830110i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 5.49842 | + | 16.9224i | 0.191199 | + | 0.588450i | 1.00000 | 0.000367397i | \(0.000116946\pi\) | |
−0.808801 | + | 0.588082i | \(0.799883\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 37.2323 | − | 27.0508i | 1.29313 | − | 0.939515i | 0.293267 | − | 0.956030i | \(-0.405257\pi\) |
0.999864 | + | 0.0165158i | \(0.00525737\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 16.2861 | + | 11.8325i | 0.564957 | + | 0.410465i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 22.0023 | + | 15.9856i | 0.762335 | + | 0.553869i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −9.91316 | + | 1.63217i | −0.343059 | + | 0.0564837i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.62299 | + | 8.07273i | −0.0906637 | + | 0.279034i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0.312751 | + | 0.962548i | 0.0107974 | + | 0.0332308i | 0.956310 | − | 0.292354i | \(-0.0944387\pi\) |
−0.945513 | + | 0.325585i | \(0.894439\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8.80731 | + | 27.1061i | −0.303700 | + | 0.934694i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 9.81651 | 0.338099 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −26.6227 | + | 4.38335i | −0.915849 | + | 0.150792i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 37.2892 | − | 27.0922i | 1.28127 | − | 0.930899i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −6.54547 | −0.224640 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8.31054 | 0.284882 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7.93916 | − | 5.76813i | 0.271832 | − | 0.197497i | −0.443515 | − | 0.896267i | \(-0.646269\pi\) |
0.715347 | + | 0.698770i | \(0.246269\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.80902 | + | 11.8910i | −0.0618671 | + | 0.406662i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −57.3424 | −1.95878 | −0.979390 | − | 0.201979i | \(-0.935263\pi\) | ||||
−0.979390 | + | 0.201979i | \(0.935263\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.31727 | − | 10.2095i | 0.113184 | − | 0.348344i | −0.878380 | − | 0.477963i | \(-0.841375\pi\) |
0.991564 | + | 0.129619i | \(0.0413754\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −14.7816 | − | 45.4932i | −0.503757 | − | 1.55040i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2.97661 | − | 9.16105i | 0.101325 | − | 0.311846i | −0.887525 | − | 0.460759i | \(-0.847577\pi\) |
0.988850 | + | 0.148913i | \(0.0475774\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.99334 | − | 2.00410i | −0.135778 | − | 0.0681415i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −9.38232 | − | 6.81665i | −0.318640 | − | 0.231506i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.32120 | + | 2.41299i | 0.112664 | + | 0.0818551i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.293932 | − | 0.213554i | 0.00995951 | − | 0.00723601i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 4.86764 | + | 14.9811i | 0.164745 | + | 0.507032i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 34.8076 | + | 33.5557i | 1.17671 | + | 1.13439i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −0.217491 | − | 0.669370i | −0.00734416 | − | 0.0226030i | 0.947317 | − | 0.320297i | \(-0.103783\pi\) |
−0.954661 | + | 0.297694i | \(0.903783\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0.703382 | − | 0.511037i | 0.0237245 | − | 0.0172369i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −8.03076 | − | 5.83469i | −0.270563 | − | 0.196576i | 0.444228 | − | 0.895914i | \(-0.353478\pi\) |
−0.714791 | + | 0.699338i | \(0.753478\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −13.6241 | − | 9.89850i | −0.458488 | − | 0.333111i | 0.334450 | − | 0.942414i | \(-0.391450\pi\) |
−0.792938 | + | 0.609302i | \(0.791450\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −14.5741 | − | 7.31419i | −0.489904 | − | 0.245864i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 14.3358 | − | 44.1212i | 0.481351 | − | 1.48144i | −0.355847 | − | 0.934544i | \(-0.615808\pi\) |
0.837198 | − | 0.546901i | \(-0.184192\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 23.3935 | + | 71.9979i | 0.784594 | + | 2.41473i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.180557 | − | 0.555698i | 0.00604890 | − | 0.0186166i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −48.7837 | −1.63249 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.70141 | − | 30.9031i | 0.157151 | − | 1.03298i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.06168 | + | 0.771358i | −0.0354486 | + | 0.0257549i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −5.99572 | −0.199968 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −20.7004 | −0.689630 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −24.5972 | + | 17.8709i | −0.818543 | + | 0.594706i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 29.8696 | − | 4.91794i | 0.992899 | − | 0.163478i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 28.5101 | 0.946662 | 0.473331 | − | 0.880885i | \(-0.343051\pi\) | ||||
0.473331 | + | 0.880885i | \(0.343051\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.20693 | − | 6.79224i | 0.0731993 | − | 0.225284i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.00884 | − | 6.18256i | −0.0665557 | − | 0.204837i | 0.912248 | − | 0.409639i | \(-0.134345\pi\) |
−0.978804 | + | 0.204801i | \(0.934345\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.90901 | − | 8.95301i | 0.0962742 | − | 0.296301i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 10.6208 | − | 1.74868i | 0.351112 | − | 0.0578095i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 66.0029 | + | 47.9539i | 2.17961 | + | 1.58358i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −13.6130 | − | 9.89041i | −0.449051 | − | 0.326255i | 0.340170 | − | 0.940364i | \(-0.389515\pi\) |
−0.789221 | + | 0.614109i | \(0.789515\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 17.5768 | − | 12.7703i | 0.579174 | − | 0.420795i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3.15326 | + | 9.70474i | 0.103791 | + | 0.319436i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 29.2112 | + | 9.09862i | 0.960459 | + | 0.299161i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0.409613 | + | 1.26066i | 0.0134534 | + | 0.0414054i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 25.5979 | − | 18.5979i | 0.839839 | − | 0.610179i | −0.0824866 | − | 0.996592i | \(-0.526286\pi\) |
0.922326 | + | 0.386413i | \(0.126286\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 50.9165 | + | 36.9930i | 1.66872 | + | 1.21240i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 15.3576 | + | 11.1580i | 0.502787 | + | 0.365296i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.39520 | − | 2.69742i | −0.0456281 | − | 0.0882149i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −0.726513 | + | 2.23598i | −0.0237341 | + | 0.0730462i | −0.962222 | − | 0.272266i | \(-0.912227\pi\) |
0.938488 | + | 0.345312i | \(0.112227\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.87947 | + | 5.78443i | 0.0613343 | + | 0.188768i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.32816 | − | 4.08766i | 0.0432968 | − | 0.133254i | −0.927071 | − | 0.374885i | \(-0.877682\pi\) |
0.970368 | + | 0.241631i | \(0.0776823\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −15.0230 | −0.489217 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 8.64235 | + | 4.33726i | 0.281136 | + | 0.141091i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −22.5245 | + | 16.3650i | −0.731948 | + | 0.531791i | −0.890179 | − | 0.455611i | \(-0.849421\pi\) |
0.158231 | + | 0.987402i | \(0.449421\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.206176 | 0.00669275 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.97817 | −0.0641467 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 36.0991 | − | 26.2275i | 1.16936 | − | 0.849593i | 0.178432 | − | 0.983952i | \(-0.442898\pi\) |
0.990933 | + | 0.134359i | \(0.0428976\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.61495 | + | 5.05561i | 0.0846178 | + | 0.163596i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.412724 | 0.0133415 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 17.7072 | − | 54.4971i | 0.571795 | − | 1.75980i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 12.6848 | + | 39.0399i | 0.409188 | + | 1.25935i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 5.46328 | − | 16.8143i | 0.176052 | − | 0.541832i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −8.80867 | + | 8.91686i | −0.283561 | + | 0.287044i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 44.6460 | + | 32.4372i | 1.43572 | + | 1.04311i | 0.988916 | + | 0.148479i | \(0.0474378\pi\) |
0.446804 | + | 0.894632i | \(0.352562\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 10.1151 | + | 7.34902i | 0.324942 | + | 0.236084i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5.00915 | − | 3.63936i | 0.160751 | − | 0.116793i | −0.504502 | − | 0.863411i | \(-0.668324\pi\) |
0.665253 | + | 0.746618i | \(0.268324\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −22.5871 | − | 69.5160i | −0.724109 | − | 2.22858i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −4.57628 | + | 1.54893i | −0.146558 | + | 0.0496056i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 7.46728 | + | 22.9819i | 0.238900 | + | 0.735257i | 0.996580 | + | 0.0826317i | \(0.0263325\pi\) |
−0.757681 | + | 0.652626i | \(0.773667\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.62719 | − | 4.81494i | 0.211806 | − | 0.153886i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.86374 | − | 2.08063i | −0.0914321 | − | 0.0664293i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 7.70430 | + | 5.59750i | 0.245729 | + | 0.178533i | 0.703832 | − | 0.710367i | \(-0.251471\pi\) |
−0.458103 | + | 0.888899i | \(0.651471\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.64214 | + | 17.3672i | −0.0841854 | + | 0.553364i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −12.1194 | + | 37.2998i | −0.385766 | + | 1.18727i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.95072 | + | 9.08137i | 0.0938273 | + | 0.288771i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.21741 | + | 9.90216i | −0.102204 | + | 0.314553i | −0.989064 | − | 0.147486i | \(-0.952882\pi\) |
0.886860 | + | 0.462039i | \(0.152882\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 13.1307 | 0.416691 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −26.7101 | + | 27.0382i | −0.846768 | + | 0.857168i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 46.7359 | − | 33.9556i | 1.48014 | − | 1.07539i | 0.502629 | − | 0.864502i | \(-0.332366\pi\) |
0.977511 | − | 0.210883i | \(-0.0676340\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 6.11909 | 0.193599 |
(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 | 300.2.m.b.181.1 | yes | 8 | |
3.2 | odd | 2 | 900.2.n.b.181.2 | 8 | |||
5.2 | odd | 4 | 1500.2.o.b.349.2 | 16 | |||
5.3 | odd | 4 | 1500.2.o.b.349.3 | 16 | |||
5.4 | even | 2 | 1500.2.m.a.901.1 | 8 | |||
25.2 | odd | 20 | 7500.2.d.c.1249.8 | 8 | |||
25.3 | odd | 20 | 1500.2.o.b.649.1 | 16 | |||
25.4 | even | 10 | 1500.2.m.a.601.1 | 8 | |||
25.11 | even | 5 | 7500.2.a.e.1.4 | 4 | |||
25.14 | even | 10 | 7500.2.a.f.1.1 | 4 | |||
25.21 | even | 5 | inner | 300.2.m.b.121.1 | ✓ | 8 | |
25.22 | odd | 20 | 1500.2.o.b.649.4 | 16 | |||
25.23 | odd | 20 | 7500.2.d.c.1249.1 | 8 | |||
75.71 | odd | 10 | 900.2.n.b.721.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
300.2.m.b.121.1 | ✓ | 8 | 25.21 | even | 5 | inner | |
300.2.m.b.181.1 | yes | 8 | 1.1 | even | 1 | trivial | |
900.2.n.b.181.2 | 8 | 3.2 | odd | 2 | |||
900.2.n.b.721.2 | 8 | 75.71 | odd | 10 | |||
1500.2.m.a.601.1 | 8 | 25.4 | even | 10 | |||
1500.2.m.a.901.1 | 8 | 5.4 | even | 2 | |||
1500.2.o.b.349.2 | 16 | 5.2 | odd | 4 | |||
1500.2.o.b.349.3 | 16 | 5.3 | odd | 4 | |||
1500.2.o.b.649.1 | 16 | 25.3 | odd | 20 | |||
1500.2.o.b.649.4 | 16 | 25.22 | odd | 20 | |||
7500.2.a.e.1.4 | 4 | 25.11 | even | 5 | |||
7500.2.a.f.1.1 | 4 | 25.14 | even | 10 | |||
7500.2.d.c.1249.1 | 8 | 25.23 | odd | 20 | |||
7500.2.d.c.1249.8 | 8 | 25.2 | odd | 20 |