Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3024,2,Mod(2305,3024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3024, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3024.2305");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3024.q (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(24.1467615712\) |
Analytic rank: | \(0\) |
Dimension: | \(22\) |
Relative dimension: | \(11\) over \(\Q(\zeta_{3})\) |
Twist minimal: | no (minimal twist has level 504) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 2305.2 | ||
Character | \(\chi\) | \(=\) | 3024.2305 |
Dual form | 3024.2.q.k.2881.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1135\) | \(2593\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.71796 | − | 2.97559i | −0.768294 | − | 1.33072i | −0.938487 | − | 0.345314i | \(-0.887773\pi\) |
0.170193 | − | 0.985411i | \(-0.445561\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.727932 | + | 2.54364i | 0.275132 | + | 0.961406i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.20469 | + | 3.81863i | −0.664739 | + | 1.15136i | 0.314618 | + | 0.949219i | \(0.398124\pi\) |
−0.979356 | + | 0.202143i | \(0.935210\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.49401 | − | 2.58771i | 0.414365 | − | 0.717701i | −0.580997 | − | 0.813906i | \(-0.697337\pi\) |
0.995362 | + | 0.0962048i | \(0.0306704\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.542270 | − | 0.939239i | −0.131520 | − | 0.227799i | 0.792743 | − | 0.609556i | \(-0.208652\pi\) |
−0.924263 | + | 0.381757i | \(0.875319\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.74273 | − | 6.48261i | 0.858642 | − | 1.48721i | −0.0145824 | − | 0.999894i | \(-0.504642\pi\) |
0.873225 | − | 0.487318i | \(-0.162025\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.16279 | + | 3.74606i | 0.450972 | + | 0.781107i | 0.998447 | − | 0.0557153i | \(-0.0177439\pi\) |
−0.547474 | + | 0.836823i | \(0.684411\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.40276 | + | 5.89375i | −0.680552 | + | 1.17875i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.68485 | − | 2.91825i | −0.312870 | − | 0.541906i | 0.666113 | − | 0.745851i | \(-0.267957\pi\) |
−0.978982 | + | 0.203945i | \(0.934624\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.37469 | −1.68374 | −0.841872 | − | 0.539678i | \(-0.818546\pi\) | ||||
−0.841872 | + | 0.539678i | \(0.818546\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 6.31828 | − | 6.53590i | 1.06798 | − | 1.10477i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.50767 | + | 4.34341i | −0.412258 | + | 0.714052i | −0.995136 | − | 0.0985079i | \(-0.968593\pi\) |
0.582878 | + | 0.812559i | \(0.301926\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.20160 | − | 2.08122i | 0.187658 | − | 0.325033i | −0.756811 | − | 0.653634i | \(-0.773244\pi\) |
0.944469 | + | 0.328601i | \(0.106577\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.31412 | − | 5.74023i | −0.505399 | − | 0.875377i | −0.999980 | − | 0.00624563i | \(-0.998012\pi\) |
0.494581 | − | 0.869131i | \(-0.335321\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.00831 | 0.438807 | 0.219403 | − | 0.975634i | \(-0.429589\pi\) | ||||
0.219403 | + | 0.975634i | \(0.429589\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.94023 | + | 3.70320i | −0.848604 | + | 0.529028i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.530699 | + | 0.919198i | 0.0728971 | + | 0.126262i | 0.900170 | − | 0.435539i | \(-0.143442\pi\) |
−0.827273 | + | 0.561801i | \(0.810109\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 15.1502 | 2.04286 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 12.4094 | 1.61557 | 0.807783 | − | 0.589480i | \(-0.200668\pi\) | ||||
0.807783 | + | 0.589480i | \(0.200668\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.42668 | −0.694816 | −0.347408 | − | 0.937714i | \(-0.612938\pi\) | ||||
−0.347408 | + | 0.937714i | \(0.612938\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −10.2666 | −1.27342 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.33998 | −0.408043 | −0.204022 | − | 0.978966i | \(-0.565401\pi\) | ||||
−0.204022 | + | 0.978966i | \(0.565401\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.9064 | −1.53171 | −0.765857 | − | 0.643011i | \(-0.777685\pi\) | ||||
−0.765857 | + | 0.643011i | \(0.777685\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.21382 | − | 14.2267i | −0.961355 | − | 1.66511i | −0.719106 | − | 0.694901i | \(-0.755448\pi\) |
−0.242249 | − | 0.970214i | \(-0.577885\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −11.3181 | − | 2.82823i | −1.28982 | − | 0.322307i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.35031 | 0.264431 | 0.132216 | − | 0.991221i | \(-0.457791\pi\) | ||||
0.132216 | + | 0.991221i | \(0.457791\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.60602 | − | 2.78171i | −0.176283 | − | 0.305332i | 0.764321 | − | 0.644836i | \(-0.223074\pi\) |
−0.940605 | + | 0.339504i | \(0.889741\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.86319 | + | 3.22715i | −0.202092 | + | 0.350033i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.67524 | + | 9.82981i | −0.601575 | + | 1.04196i | 0.391008 | + | 0.920387i | \(0.372126\pi\) |
−0.992583 | + | 0.121570i | \(0.961207\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.66974 | + | 1.91656i | 0.804008 | + | 0.200910i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −25.7194 | −2.63876 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.40321 | − | 11.0907i | −0.650148 | − | 1.12609i | −0.983087 | − | 0.183140i | \(-0.941374\pi\) |
0.332939 | − | 0.942948i | \(-0.391960\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.388110 | + | 0.672227i | −0.0386184 | + | 0.0668891i | −0.884689 | − | 0.466182i | \(-0.845629\pi\) |
0.846070 | + | 0.533072i | \(0.178962\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.14131 | + | 1.97681i | 0.112457 | + | 0.194781i | 0.916760 | − | 0.399438i | \(-0.130795\pi\) |
−0.804304 | + | 0.594219i | \(0.797461\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.27468 | + | 3.93986i | −0.219901 | + | 0.380880i | −0.954778 | − | 0.297321i | \(-0.903907\pi\) |
0.734876 | + | 0.678201i | \(0.237240\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.36710 | + | 4.09994i | 0.226727 | + | 0.392703i | 0.956836 | − | 0.290627i | \(-0.0938640\pi\) |
−0.730109 | + | 0.683331i | \(0.760531\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.175367 | + | 0.303745i | −0.0164972 | + | 0.0285740i | −0.874156 | − | 0.485645i | \(-0.838585\pi\) |
0.857659 | + | 0.514219i | \(0.171918\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.43116 | − | 12.8711i | 0.692959 | − | 1.20024i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.99435 | − | 2.06304i | 0.182822 | − | 0.189119i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.22130 | − | 7.31151i | −0.383755 | − | 0.664683i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 6.20360 | 0.554867 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.4175 | −1.10187 | −0.550935 | − | 0.834548i | \(-0.685729\pi\) | ||||
−0.550935 | + | 0.834548i | \(0.685729\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.87152 | − | 13.6339i | −0.687738 | − | 1.19120i | −0.972568 | − | 0.232619i | \(-0.925270\pi\) |
0.284830 | − | 0.958578i | \(-0.408063\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 19.2139 | + | 4.80128i | 1.66606 | + | 0.416324i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.11510 | + | 3.66346i | −0.180705 | + | 0.312990i | −0.942121 | − | 0.335274i | \(-0.891171\pi\) |
0.761416 | + | 0.648264i | \(0.224505\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.80367 | + | 16.9805i | −0.831537 | + | 1.44026i | 0.0652824 | + | 0.997867i | \(0.479205\pi\) |
−0.896819 | + | 0.442397i | \(0.854128\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6.58767 | + | 11.4102i | 0.550889 | + | 0.954167i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.78902 | + | 10.0269i | −0.480752 | + | 0.832686i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.86326 | − | 8.42341i | −0.398414 | − | 0.690073i | 0.595117 | − | 0.803639i | \(-0.297106\pi\) |
−0.993530 | + | 0.113567i | \(0.963772\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.91074 | + | 8.50565i | −0.399630 | + | 0.692180i | −0.993680 | − | 0.112248i | \(-0.964195\pi\) |
0.594050 | + | 0.804428i | \(0.297528\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 16.1053 | + | 27.8952i | 1.29361 | + | 2.24060i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −12.0408 | −0.960962 | −0.480481 | − | 0.877005i | \(-0.659538\pi\) | ||||
−0.480481 | + | 0.877005i | \(0.659538\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −7.95427 | + | 8.22824i | −0.626884 | + | 0.648476i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.885601 | + | 1.53391i | −0.0693656 | + | 0.120145i | −0.898622 | − | 0.438723i | \(-0.855431\pi\) |
0.829257 | + | 0.558868i | \(0.188764\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −7.86350 | + | 13.6200i | −0.608496 | + | 1.05395i | 0.382993 | + | 0.923751i | \(0.374893\pi\) |
−0.991489 | + | 0.130194i | \(0.958440\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.03584 | + | 3.52618i | 0.156603 | + | 0.271245i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −18.8063 | −1.42981 | −0.714907 | − | 0.699220i | \(-0.753531\pi\) | ||||
−0.714907 | + | 0.699220i | \(0.753531\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −17.4686 | − | 4.36515i | −1.32050 | − | 0.329974i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.34201 | + | 5.78853i | 0.249794 | + | 0.432655i | 0.963468 | − | 0.267822i | \(-0.0863039\pi\) |
−0.713675 | + | 0.700477i | \(0.752971\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.73726 | 0.352117 | 0.176059 | − | 0.984380i | \(-0.443665\pi\) | ||||
0.176059 | + | 0.984380i | \(0.443665\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 17.2323 | 1.26694 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.78214 | 0.349705 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −23.0693 | −1.66924 | −0.834618 | − | 0.550829i | \(-0.814312\pi\) | ||||
−0.834618 | + | 0.550829i | \(0.814312\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 18.3070 | 1.31777 | 0.658885 | − | 0.752244i | \(-0.271028\pi\) | ||||
0.658885 | + | 0.752244i | \(0.271028\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −14.5866 | −1.03925 | −0.519625 | − | 0.854395i | \(-0.673928\pi\) | ||||
−0.519625 | + | 0.854395i | \(0.673928\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.912102 | + | 1.57981i | 0.0646572 | + | 0.111990i | 0.896542 | − | 0.442959i | \(-0.146071\pi\) |
−0.831885 | + | 0.554949i | \(0.812738\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 6.19653 | − | 6.40996i | 0.434911 | − | 0.449891i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −8.25716 | −0.576705 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 16.5031 | + | 28.5843i | 1.14155 | + | 1.97721i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.77359 | − | 4.80400i | 0.190942 | − | 0.330721i | −0.754621 | − | 0.656161i | \(-0.772179\pi\) |
0.945563 | + | 0.325440i | \(0.105512\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −11.3870 | + | 19.7229i | −0.776590 | + | 1.34509i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.82413 | − | 23.8458i | −0.463252 | − | 1.61876i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.24064 | −0.217989 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.01726 | − | 10.4222i | −0.402946 | − | 0.697922i | 0.591134 | − | 0.806573i | \(-0.298680\pi\) |
−0.994080 | + | 0.108651i | \(0.965347\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6.57834 | − | 11.3940i | 0.436620 | − | 0.756248i | −0.560806 | − | 0.827947i | \(-0.689509\pi\) |
0.997426 | + | 0.0716991i | \(0.0228421\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.24159 | − | 10.8108i | −0.412456 | − | 0.714395i | 0.582702 | − | 0.812686i | \(-0.301996\pi\) |
−0.995158 | + | 0.0982915i | \(0.968662\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.01687 | − | 3.49332i | 0.132130 | − | 0.228855i | −0.792368 | − | 0.610044i | \(-0.791152\pi\) |
0.924497 | + | 0.381189i | \(0.124485\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.16814 | − | 8.95149i | −0.337133 | − | 0.583931i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 13.8679 | − | 24.0200i | 0.897043 | − | 1.55372i | 0.0657873 | − | 0.997834i | \(-0.479044\pi\) |
0.831256 | − | 0.555890i | \(-0.187623\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.9567 | + | 20.7096i | −0.770199 | + | 1.33402i | 0.167254 | + | 0.985914i | \(0.446510\pi\) |
−0.937453 | + | 0.348111i | \(0.886823\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 21.2243 | + | 11.3138i | 1.35597 | + | 0.722809i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −11.1834 | − | 19.3702i | −0.711582 | − | 1.23250i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.33510 | −0.210509 | −0.105255 | − | 0.994445i | \(-0.533566\pi\) | ||||
−0.105255 | + | 0.994445i | \(0.533566\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −19.0731 | −1.19912 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −10.9345 | − | 18.9392i | −0.682078 | − | 1.18139i | −0.974346 | − | 0.225057i | \(-0.927743\pi\) |
0.292268 | − | 0.956336i | \(-0.405590\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −12.8735 | − | 3.21690i | −0.799919 | − | 0.199889i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.75522 | + | 4.77218i | −0.169894 | + | 0.294265i | −0.938382 | − | 0.345599i | \(-0.887676\pi\) |
0.768488 | + | 0.639864i | \(0.221009\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.82344 | − | 3.15829i | 0.112013 | − | 0.194012i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3.37393 | − | 5.84382i | −0.205712 | − | 0.356304i | 0.744647 | − | 0.667458i | \(-0.232618\pi\) |
−0.950359 | + | 0.311154i | \(0.899284\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.21944 | + | 10.7724i | −0.377804 | + | 0.654376i | −0.990742 | − | 0.135755i | \(-0.956654\pi\) |
0.612938 | + | 0.790131i | \(0.289987\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −15.0040 | − | 25.9878i | −0.904778 | − | 1.56712i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.85945 | − | 8.41681i | 0.291976 | − | 0.505717i | −0.682301 | − | 0.731071i | \(-0.739021\pi\) |
0.974277 | + | 0.225354i | \(0.0723539\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.66772 | + | 16.7450i | 0.576728 | + | 0.998922i | 0.995852 | + | 0.0909928i | \(0.0290040\pi\) |
−0.419124 | + | 0.907929i | \(0.637663\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.30900 | −0.493919 | −0.246959 | − | 0.969026i | \(-0.579431\pi\) | ||||
−0.246959 | + | 0.969026i | \(0.579431\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.16857 | + | 1.54144i | 0.364119 | + | 0.0909882i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.91189 | − | 13.7038i | 0.465405 | − | 0.806105i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3.97318 | − | 6.88175i | 0.232116 | − | 0.402036i | −0.726315 | − | 0.687362i | \(-0.758769\pi\) |
0.958430 | + | 0.285326i | \(0.0921019\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −21.3188 | − | 36.9253i | −1.24123 | − | 2.14987i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 12.9249 | 0.747469 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 12.1886 | − | 12.6084i | 0.702541 | − | 0.726739i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 9.32281 | + | 16.1476i | 0.533823 | + | 0.924608i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 26.9180 | 1.53629 | 0.768145 | − | 0.640276i | \(-0.221180\pi\) | ||||
0.768145 | + | 0.640276i | \(0.221180\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.34917 | 0.530143 | 0.265071 | − | 0.964229i | \(-0.414604\pi\) | ||||
0.265071 | + | 0.964229i | \(0.414604\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 15.8380 | 0.895219 | 0.447610 | − | 0.894229i | \(-0.352275\pi\) | ||||
0.447610 | + | 0.894229i | \(0.352275\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 28.4591 | 1.59843 | 0.799213 | − | 0.601049i | \(-0.205250\pi\) | ||||
0.799213 | + | 0.601049i | \(0.205250\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 14.8583 | 0.831906 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −8.11829 | −0.451714 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 10.1675 | + | 17.6107i | 0.563994 | + | 0.976865i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.18984 | + | 7.65205i | 0.120730 | + | 0.421871i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 19.5904 | 1.07679 | 0.538393 | − | 0.842694i | \(-0.319032\pi\) | ||||
0.538393 | + | 0.842694i | \(0.319032\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5.73794 | + | 9.93841i | 0.313497 | + | 0.542993i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.73059 | − | 15.1218i | 0.475586 | − | 0.823739i | −0.524023 | − | 0.851704i | \(-0.675569\pi\) |
0.999609 | + | 0.0279654i | \(0.00890283\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 20.6683 | − | 35.7985i | 1.11925 | − | 1.93860i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −13.7437 | − | 12.4141i | −0.742090 | − | 0.670301i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −19.4502 | −1.04414 | −0.522070 | − | 0.852903i | \(-0.674840\pi\) | ||||
−0.522070 | + | 0.852903i | \(0.674840\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6.91419 | + | 11.9757i | 0.370108 | + | 0.641046i | 0.989582 | − | 0.143971i | \(-0.0459872\pi\) |
−0.619474 | + | 0.785018i | \(0.712654\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5.92295 | − | 10.2588i | 0.315247 | − | 0.546023i | −0.664243 | − | 0.747517i | \(-0.731246\pi\) |
0.979490 | + | 0.201493i | \(0.0645794\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 22.1727 | + | 38.4043i | 1.17681 | + | 2.03829i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −0.628489 | + | 1.08858i | −0.0331704 | + | 0.0574528i | −0.882134 | − | 0.470998i | \(-0.843894\pi\) |
0.848964 | + | 0.528451i | \(0.177227\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.5161 | − | 32.0709i | −0.974533 | − | 1.68794i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −28.2220 | + | 48.8819i | −1.47721 | + | 2.55860i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −7.61928 | + | 13.1970i | −0.397723 | + | 0.688877i | −0.993445 | − | 0.114314i | \(-0.963533\pi\) |
0.595721 | + | 0.803191i | \(0.296866\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.95180 | + | 2.01902i | −0.101332 | + | 0.104822i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8.66756 | − | 15.0127i | −0.448789 | − | 0.777326i | 0.549518 | − | 0.835482i | \(-0.314811\pi\) |
−0.998308 | + | 0.0581556i | \(0.981478\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −10.0688 | −0.518569 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −15.6319 | −0.802955 | −0.401478 | − | 0.915869i | \(-0.631503\pi\) | ||||
−0.401478 | + | 0.915869i | \(0.631503\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 8.90615 | + | 15.4259i | 0.455083 | + | 0.788227i | 0.998693 | − | 0.0511113i | \(-0.0162763\pi\) |
−0.543610 | + | 0.839338i | \(0.682943\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 11.0284 | + | 38.5368i | 0.562057 | + | 1.96402i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 14.7074 | − | 25.4740i | 0.745695 | − | 1.29158i | −0.204175 | − | 0.978934i | \(-0.565451\pi\) |
0.949869 | − | 0.312647i | \(-0.101216\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.34563 | − | 4.06275i | 0.118624 | − | 0.205462i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4.03774 | − | 6.99357i | −0.203161 | − | 0.351885i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.55930 | + | 2.70079i | −0.0782592 | + | 0.135549i | −0.902499 | − | 0.430692i | \(-0.858270\pi\) |
0.824240 | + | 0.566241i | \(0.191603\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −17.8613 | − | 30.9367i | −0.891950 | − | 1.54490i | −0.837534 | − | 0.546385i | \(-0.816004\pi\) |
−0.0544157 | − | 0.998518i | \(-0.517330\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −14.0059 | + | 24.2590i | −0.697684 | + | 1.20842i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −11.0572 | − | 19.1517i | −0.548087 | − | 0.949315i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9.81652 | 0.485396 | 0.242698 | − | 0.970102i | \(-0.421968\pi\) | ||||
0.242698 | + | 0.970102i | \(0.421968\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 9.03320 | + | 31.5651i | 0.444494 | + | 1.55321i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.51814 | + | 9.55771i | −0.270875 | + | 0.469169i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.09812 | − | 10.5623i | 0.297913 | − | 0.516000i | −0.677746 | − | 0.735297i | \(-0.737043\pi\) |
0.975658 | + | 0.219297i | \(0.0703762\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.10015 | − | 8.83373i | −0.248566 | − | 0.430529i | 0.714562 | − | 0.699572i | \(-0.246626\pi\) |
−0.963128 | + | 0.269043i | \(0.913293\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 7.38085 | 0.358024 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.95026 | − | 13.8035i | −0.191166 | − | 0.668000i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.70254 | − | 9.87710i | −0.274682 | − | 0.475763i | 0.695373 | − | 0.718649i | \(-0.255239\pi\) |
−0.970055 | + | 0.242886i | \(0.921906\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 26.2391 | 1.26097 | 0.630486 | − | 0.776201i | \(-0.282856\pi\) | ||||
0.630486 | + | 0.776201i | \(0.282856\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 32.3790 | 1.54890 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −22.9554 | −1.09560 | −0.547801 | − | 0.836609i | \(-0.684535\pi\) | ||||
−0.547801 | + | 0.836609i | \(0.684535\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 22.4025 | 1.06438 | 0.532188 | − | 0.846626i | \(-0.321370\pi\) | ||||
0.532188 | + | 0.846626i | \(0.321370\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 38.9993 | 1.84874 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −17.0576 | −0.805000 | −0.402500 | − | 0.915420i | \(-0.631859\pi\) | ||||
−0.402500 | + | 0.915420i | \(0.631859\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.29829 | + | 9.17690i | 0.249487 | + | 0.432123i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −7.47340 | − | 26.1146i | −0.350358 | − | 1.22427i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9.54729 | 0.446604 | 0.223302 | − | 0.974749i | \(-0.428316\pi\) | ||||
0.223302 | + | 0.974749i | \(0.428316\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −10.1213 | − | 17.5305i | −0.471394 | − | 0.816478i | 0.528070 | − | 0.849201i | \(-0.322916\pi\) |
−0.999464 | + | 0.0327222i | \(0.989582\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.81948 | − | 13.5437i | 0.363402 | − | 0.629431i | −0.625116 | − | 0.780532i | \(-0.714948\pi\) |
0.988518 | + | 0.151101i | \(0.0482818\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2.96638 | + | 5.13793i | −0.137268 | + | 0.237755i | −0.926461 | − | 0.376390i | \(-0.877165\pi\) |
0.789194 | + | 0.614144i | \(0.210499\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.43128 | − | 8.49571i | −0.112266 | − | 0.392295i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 29.2264 | 1.34383 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 25.4712 | + | 44.1175i | 1.16870 | + | 2.02425i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 8.69708 | − | 15.0638i | 0.397380 | − | 0.688282i | −0.596022 | − | 0.802968i | \(-0.703253\pi\) |
0.993402 | + | 0.114686i | \(0.0365862\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.49298 | + | 12.9782i | 0.341650 | + | 0.591756i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −22.0009 | + | 38.1067i | −0.999009 | + | 1.73033i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9.76967 | + | 16.9216i | 0.442706 | + | 0.766790i | 0.997889 | − | 0.0649386i | \(-0.0206851\pi\) |
−0.555183 | + | 0.831728i | \(0.687352\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.16702 | + | 10.6816i | −0.278314 | + | 0.482054i | −0.970966 | − | 0.239218i | \(-0.923109\pi\) |
0.692652 | + | 0.721272i | \(0.256442\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.82729 | + | 3.16496i | −0.0822971 | + | 0.142543i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −9.39502 | − | 32.8294i | −0.421424 | − | 1.47260i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9.27308 | + | 16.0614i | 0.415120 | + | 0.719009i | 0.995441 | − | 0.0953788i | \(-0.0304062\pi\) |
−0.580321 | + | 0.814388i | \(0.697073\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −14.3264 | −0.638782 | −0.319391 | − | 0.947623i | \(-0.603478\pi\) | ||||
−0.319391 | + | 0.947623i | \(0.603478\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.66703 | 0.118681 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −8.43056 | − | 14.6022i | −0.373678 | − | 0.647229i | 0.616450 | − | 0.787394i | \(-0.288570\pi\) |
−0.990128 | + | 0.140165i | \(0.955237\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 30.2087 | − | 31.2491i | 1.33635 | − | 1.38238i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.92145 | − | 6.79215i | 0.172800 | − | 0.299298i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6.63238 | + | 11.4876i | −0.291692 | + | 0.505225i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10.8132 | − | 18.7291i | −0.473737 | − | 0.820536i | 0.525811 | − | 0.850601i | \(-0.323762\pi\) |
−0.999548 | + | 0.0300652i | \(0.990428\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8.27472 | + | 14.3322i | −0.361828 | + | 0.626705i | −0.988262 | − | 0.152770i | \(-0.951181\pi\) |
0.626433 | + | 0.779475i | \(0.284514\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 5.08361 | + | 8.80507i | 0.221446 | + | 0.383555i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.14470 | − | 3.71472i | 0.0932476 | − | 0.161510i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.59040 | − | 6.21876i | −0.155517 | − | 0.269364i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 15.6312 | 0.675796 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.04479 | − | 30.8480i | −0.0450025 | − | 1.32872i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −11.9542 | + | 20.7053i | −0.513952 | + | 0.890191i | 0.485917 | + | 0.874005i | \(0.338486\pi\) |
−0.999869 | + | 0.0161861i | \(0.994848\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 8.13317 | − | 14.0871i | 0.348387 | − | 0.603423i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14.8193 | + | 25.6678i | 0.633627 | + | 1.09747i | 0.986804 | + | 0.161918i | \(0.0517679\pi\) |
−0.353177 | + | 0.935556i | \(0.614899\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −25.2238 | −1.07457 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.71087 | + | 5.97836i | 0.0727536 | + | 0.254226i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 10.8366 | + | 18.7695i | 0.459160 | + | 0.795288i | 0.998917 | − | 0.0465330i | \(-0.0148173\pi\) |
−0.539757 | + | 0.841821i | \(0.681484\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −19.8054 | −0.837679 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 14.1556 | 0.596589 | 0.298294 | − | 0.954474i | \(-0.403582\pi\) | ||||
0.298294 | + | 0.954474i | \(0.403582\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.20510 | 0.0506988 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 34.0356 | 1.42684 | 0.713422 | − | 0.700734i | \(-0.247144\pi\) | ||||
0.713422 | + | 0.700734i | \(0.247144\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.34970 | 0.223878 | 0.111939 | − | 0.993715i | \(-0.464294\pi\) | ||||
0.111939 | + | 0.993715i | \(0.464294\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −29.4378 | −1.22764 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 11.1865 | + | 19.3756i | 0.465699 | + | 0.806615i | 0.999233 | − | 0.0391640i | \(-0.0124695\pi\) |
−0.533533 | + | 0.845779i | \(0.679136\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.90659 | − | 6.11003i | 0.245047 | − | 0.253487i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.68011 | −0.193830 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −2.49899 | − | 4.32839i | −0.103145 | − | 0.178652i | 0.809834 | − | 0.586659i | \(-0.199557\pi\) |
−0.912979 | + | 0.408007i | \(0.866224\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −35.0870 | + | 60.7724i | −1.44573 | + | 2.50408i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −12.1698 | + | 21.0788i | −0.499755 | + | 0.865601i | −1.00000 | 0.000282582i | \(-0.999910\pi\) | |
0.500245 | + | 0.865884i | \(0.333243\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −9.56498 | − | 2.39015i | −0.392126 | − | 0.0979868i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 46.2145 | 1.88827 | 0.944137 | − | 0.329552i | \(-0.106898\pi\) | ||||
0.944137 | + | 0.329552i | \(0.106898\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −16.6163 | − | 28.7803i | −0.677792 | − | 1.17397i | −0.975644 | − | 0.219359i | \(-0.929603\pi\) |
0.297852 | − | 0.954612i | \(-0.403730\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −14.5040 | + | 25.1217i | −0.589673 | + | 1.02134i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 21.9318 | + | 37.9869i | 0.890182 | + | 1.54184i | 0.839656 | + | 0.543118i | \(0.182756\pi\) |
0.0505262 | + | 0.998723i | \(0.483910\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.49445 | − | 7.78462i | 0.181826 | − | 0.314932i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.81569 | + | 3.14487i | 0.0733351 | + | 0.127020i | 0.900361 | − | 0.435144i | \(-0.143302\pi\) |
−0.827026 | + | 0.562164i | \(0.809969\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −10.4542 | + | 18.1073i | −0.420872 | + | 0.728971i | −0.996025 | − | 0.0890744i | \(-0.971609\pi\) |
0.575153 | + | 0.818046i | \(0.304942\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 11.9745 | − | 20.7405i | 0.481296 | − | 0.833629i | −0.518474 | − | 0.855094i | \(-0.673500\pi\) |
0.999770 | + | 0.0214645i | \(0.00683289\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −29.1347 | − | 7.28035i | −1.16726 | − | 0.291681i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 6.35626 | + | 11.0094i | 0.254251 | + | 0.440375i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5.43933 | 0.216880 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.06918 | 0.241610 | 0.120805 | − | 0.992676i | \(-0.461452\pi\) | ||||
0.120805 | + | 0.992676i | \(0.461452\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 21.3327 | + | 36.9492i | 0.846561 | + | 1.46629i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.708008 | + | 20.9042i | 0.0280523 | + | 0.828255i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −8.69407 | + | 15.0586i | −0.343395 | + | 0.594778i | −0.985061 | − | 0.172207i | \(-0.944910\pi\) |
0.641666 | + | 0.766984i | \(0.278244\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −9.66411 | + | 16.7387i | −0.381115 | + | 0.660111i | −0.991222 | − | 0.132208i | \(-0.957793\pi\) |
0.610107 | + | 0.792319i | \(0.291127\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 12.7041 | + | 22.0042i | 0.499451 | + | 0.865075i | 1.00000 | 0.000633482i | \(-0.000201644\pi\) | |
−0.500549 | + | 0.865708i | \(0.666868\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −27.3588 | + | 47.3869i | −1.07393 | + | 1.86010i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −12.9064 | − | 22.3545i | −0.505065 | − | 0.874799i | −0.999983 | − | 0.00585902i | \(-0.998135\pi\) |
0.494917 | − | 0.868940i | \(-0.335198\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −27.0459 | + | 46.8449i | −1.05677 | + | 1.83038i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 8.62598 | + | 14.9406i | 0.336020 | + | 0.582004i | 0.983680 | − | 0.179925i | \(-0.0575856\pi\) |
−0.647660 | + | 0.761930i | \(0.724252\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12.9635 | 0.504222 | 0.252111 | − | 0.967698i | \(-0.418875\pi\) | ||||
0.252111 | + | 0.967698i | \(0.418875\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −18.7220 | − | 65.4210i | −0.726008 | − | 2.53692i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.28797 | − | 12.6231i | 0.282191 | − | 0.488769i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 11.9641 | − | 20.7225i | 0.461871 | − | 0.799984i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −20.8060 | − | 36.0371i | −0.802013 | − | 1.38913i | −0.918289 | − | 0.395910i | \(-0.870429\pi\) |
0.116277 | − | 0.993217i | \(-0.462904\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 22.1998 | 0.853209 | 0.426605 | − | 0.904438i | \(-0.359710\pi\) | ||||
0.426605 | + | 0.904438i | \(0.359710\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 23.5496 | − | 24.3607i | 0.903752 | − | 0.934879i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −4.60315 | − | 7.97289i | −0.176135 | − | 0.305074i | 0.764419 | − | 0.644720i | \(-0.223026\pi\) |
−0.940553 | + | 0.339646i | \(0.889693\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 14.5346 | 0.555338 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.17149 | 0.120824 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 40.0585 | 1.52390 | 0.761949 | − | 0.647636i | \(-0.224242\pi\) | ||||
0.761949 | + | 0.647636i | \(0.224242\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 67.3692 | 2.55546 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.60636 | −0.0987228 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −34.3868 | −1.29877 | −0.649385 | − | 0.760459i | \(-0.724974\pi\) | ||||
−0.649385 | + | 0.760459i | \(0.724974\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 18.7711 | + | 32.5124i | 0.707964 | + | 1.22623i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.99242 | − | 0.497878i | −0.0749328 | − | 0.0187246i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 21.1840 | 0.795582 | 0.397791 | − | 0.917476i | \(-0.369777\pi\) | ||||
0.397791 | + | 0.917476i | \(0.369777\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −20.2755 | − | 35.1181i | −0.759322 | − | 1.31518i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 22.6347 | − | 39.2044i | 0.846489 | − | 1.46616i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −21.5994 | + | 37.4113i | −0.805523 | + | 1.39521i | 0.110414 | + | 0.993886i | \(0.464782\pi\) |
−0.915937 | + | 0.401321i | \(0.868551\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.19750 | + | 4.34207i | −0.156323 | + | 0.161707i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 22.9326 | 0.851696 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −20.5571 | − | 35.6059i | −0.762420 | − | 1.32055i | −0.941600 | − | 0.336734i | \(-0.890678\pi\) |
0.179180 | − | 0.983816i | \(-0.442656\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.59430 | + | 6.22551i | −0.132940 | + | 0.230259i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −26.0425 | − | 45.1070i | −0.961903 | − | 1.66607i | −0.717715 | − | 0.696337i | \(-0.754812\pi\) |
−0.244189 | − | 0.969728i | \(-0.578522\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 7.36361 | − | 12.7541i | 0.271242 | − | 0.469805i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −7.18624 | − | 12.4469i | −0.264350 | − | 0.457868i | 0.703043 | − | 0.711147i | \(-0.251824\pi\) |
−0.967393 | + | 0.253279i | \(0.918491\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −21.3167 | + | 36.9216i | −0.782034 | + | 1.35452i | 0.148721 | + | 0.988879i | \(0.452484\pi\) |
−0.930755 | + | 0.365643i | \(0.880849\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −16.7097 | + | 28.9421i | −0.612198 | + | 1.06036i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −11.6774 | − | 2.91802i | −0.426683 | − | 0.106622i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −18.9846 | − | 32.8823i | −0.692758 | − | 1.19989i | −0.970931 | − | 0.239360i | \(-0.923062\pi\) |
0.278173 | − | 0.960531i | \(-0.410271\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 33.7458 | 1.22813 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 27.6692 | 1.00565 | 0.502827 | − | 0.864387i | \(-0.332293\pi\) | ||||
0.502827 | + | 0.864387i | \(0.332293\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 5.97210 | + | 10.3440i | 0.216488 | + | 0.374969i | 0.953732 | − | 0.300658i | \(-0.0972063\pi\) |
−0.737244 | + | 0.675627i | \(0.763873\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8.70570 | + | 9.00554i | −0.315167 | + | 0.326023i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 18.5398 | − | 32.1119i | 0.669434 | − | 1.15949i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −17.4026 | + | 30.1422i | −0.627554 | + | 1.08695i | 0.360487 | + | 0.932764i | \(0.382610\pi\) |
−0.988041 | + | 0.154191i | \(0.950723\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 13.5014 | + | 23.3851i | 0.485611 | + | 0.841103i | 0.999863 | − | 0.0165363i | \(-0.00526391\pi\) |
−0.514253 | + | 0.857639i | \(0.671931\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 31.8998 | − | 55.2521i | 1.14587 | − | 1.98471i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −8.99450 | − | 15.5789i | −0.322261 | − | 0.558173i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 28.4547 | − | 49.2850i | 1.01819 | − | 1.76356i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 20.6856 | + | 35.8286i | 0.738302 | + | 1.27878i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −21.2840 | −0.758693 | −0.379347 | − | 0.925255i | \(-0.623851\pi\) | ||||
−0.379347 | + | 0.925255i | \(0.623851\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.900275 | − | 0.224966i | −0.0320101 | − | 0.00799887i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −8.10754 | + | 14.0427i | −0.287907 | + | 0.498670i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 10.3062 | − | 17.8508i | 0.365064 | − | 0.632309i | −0.623723 | − | 0.781646i | \(-0.714381\pi\) |
0.988786 | + | 0.149337i | \(0.0477138\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.63131 | − | 2.82552i | −0.0577117 | − | 0.0999597i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 72.4356 | 2.55620 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 38.1490 | + | 9.53289i | 1.34457 | + | 0.335990i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.54223 | − | 4.40328i | −0.0893802 | − | 0.154811i | 0.817869 | − | 0.575404i | \(-0.195155\pi\) |
−0.907249 | + | 0.420593i | \(0.861822\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 7.58775 | 0.266442 | 0.133221 | − | 0.991086i | \(-0.457468\pi\) | ||||
0.133221 | + | 0.991086i | \(0.457468\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6.08570 | 0.213173 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −49.6155 | −1.73583 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −20.2696 | −0.707413 | −0.353706 | − | 0.935357i | \(-0.615079\pi\) | ||||
−0.353706 | + | 0.935357i | \(0.615079\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −21.7911 | −0.759588 | −0.379794 | − | 0.925071i | \(-0.624005\pi\) | ||||
−0.379794 | + | 0.925071i | \(0.624005\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 26.3796 | 0.917307 | 0.458654 | − | 0.888615i | \(-0.348332\pi\) | ||||
0.458654 | + | 0.888615i | \(0.348332\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 9.33400 | + | 16.1670i | 0.324183 | + | 0.561502i | 0.981347 | − | 0.192246i | \(-0.0615773\pi\) |
−0.657164 | + | 0.753748i | \(0.728244\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.69940 | + | 3.57116i | 0.232120 | + | 0.123733i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 54.0366 | 1.87001 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 12.5265 | + | 21.6966i | 0.432464 | + | 0.749050i | 0.997085 | − | 0.0763004i | \(-0.0243108\pi\) |
−0.564621 | + | 0.825351i | \(0.690977\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 8.82253 | − | 15.2811i | 0.304225 | − | 0.526934i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 6.99499 | − | 12.1157i | 0.240635 | − | 0.416792i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 15.5250 | − | 16.0598i | 0.533447 | − | 0.551820i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −21.6942 | −0.743668 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −19.2219 | − | 33.2933i | −0.658146 | − | 1.13994i | −0.981095 | − | 0.193526i | \(-0.938008\pi\) |
0.322949 | − | 0.946416i | \(-0.395326\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −6.00299 | + | 10.3975i | −0.205058 | + | 0.355172i | −0.950151 | − | 0.311789i | \(-0.899072\pi\) |
0.745093 | + | 0.666961i | \(0.232405\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −6.30154 | − | 10.9146i | −0.215006 | − | 0.372401i | 0.738269 | − | 0.674507i | \(-0.235644\pi\) |
−0.953274 | + | 0.302106i | \(0.902310\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −0.210643 | + | 0.364845i | −0.00717038 | + | 0.0124195i | −0.869588 | − | 0.493777i | \(-0.835616\pi\) |
0.862418 | + | 0.506197i | \(0.168949\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 32.3084 | + | 55.9597i | 1.09852 | + | 1.90269i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −5.18171 | + | 8.97499i | −0.175778 | + | 0.304456i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.98997 | + | 8.64289i | −0.169079 | + | 0.292853i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.51580 | + | 15.7797i | 0.152662 | + | 0.533453i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −0.893424 | − | 1.54746i | −0.0301688 | − | 0.0522539i | 0.850547 | − | 0.525899i | \(-0.176271\pi\) |
−0.880716 | + | 0.473645i | \(0.842938\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 49.8891 | 1.68081 | 0.840403 | − | 0.541962i | \(-0.182318\pi\) | ||||
0.840403 | + | 0.541962i | \(0.182318\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −34.7935 | −1.17090 | −0.585448 | − | 0.810710i | \(-0.699081\pi\) | ||||
−0.585448 | + | 0.810710i | \(0.699081\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −11.9040 | − | 20.6184i | −0.399698 | − | 0.692297i | 0.593991 | − | 0.804472i | \(-0.297552\pi\) |
−0.993688 | + | 0.112175i | \(0.964218\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −9.03906 | − | 31.5855i | −0.303160 | − | 1.05935i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 11.2593 | − | 19.5017i | 0.376778 | − | 0.652598i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 11.4829 | − | 19.8889i | 0.383830 | − | 0.664813i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 15.7950 | + | 27.3577i | 0.526792 | + | 0.912431i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.575564 | − | 0.996907i | 0.0191748 | − | 0.0332118i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −8.13841 | − | 14.0961i | −0.270530 | − | 0.468571i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 17.1406 | − | 29.6885i | 0.569146 | − | 0.985789i | −0.427505 | − | 0.904013i | \(-0.640607\pi\) |
0.996651 | − | 0.0817761i | \(-0.0260592\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 14.9839 | + | 25.9529i | 0.496438 | + | 0.859857i | 0.999992 | − | 0.00410771i | \(-0.00130753\pi\) |
−0.503553 | + | 0.863964i | \(0.667974\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 14.1631 | 0.468730 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 28.9498 | − | 29.9469i | 0.956006 | − | 0.988933i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0.391037 | − | 0.677296i | 0.0128991 | − | 0.0223419i | −0.859504 | − | 0.511129i | \(-0.829227\pi\) |
0.872403 | + | 0.488787i | \(0.162561\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −19.2824 | + | 33.3981i | −0.634688 | + | 1.09931i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −17.0660 | − | 29.5591i | −0.561126 | − | 0.971898i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 13.5324 | 0.443983 | 0.221992 | − | 0.975049i | \(-0.428744\pi\) | ||||
0.221992 | + | 0.975049i | \(0.428744\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.77367 | + | 52.3683i | 0.0581297 | + | 1.71630i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −8.21552 | − | 14.2297i | −0.268676 | − | 0.465361i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.27674 | −0.0743777 | −0.0371889 | − | 0.999308i | \(-0.511840\pi\) | ||||
−0.0371889 | + | 0.999308i | \(0.511840\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 8.15440 | 0.265826 | 0.132913 | − | 0.991128i | \(-0.457567\pi\) | ||||
0.132913 | + | 0.991128i | \(0.457567\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 10.3952 | 0.338514 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 7.87106 | 0.255775 | 0.127888 | − | 0.991789i | \(-0.459180\pi\) | ||||
0.127888 | + | 0.991789i | \(0.459180\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −49.0862 | −1.59341 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −43.1097 | −1.39646 | −0.698230 | − | 0.715873i | \(-0.746029\pi\) | ||||
−0.698230 | + | 0.715873i | \(0.746029\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 39.6321 | + | 68.6448i | 1.28246 | + | 2.22129i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −10.8582 | − | 2.71330i | −0.350629 | − | 0.0876172i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 56.8847 | 1.83499 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −31.4507 | − | 54.4742i | −1.01243 | − | 1.75359i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −13.9537 | + | 24.1684i | −0.448719 | + | 0.777205i | −0.998303 | − | 0.0582340i | \(-0.981453\pi\) |
0.549584 | + | 0.835439i | \(0.314786\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 21.0705 | − | 36.4952i | 0.676185 | − | 1.17119i | −0.299936 | − | 0.953959i | \(-0.596965\pi\) |
0.976121 | − | 0.217228i | \(-0.0697015\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −50.3286 | − | 12.5764i | −1.61346 | − | 0.403181i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 13.8549 | 0.443259 | 0.221629 | − | 0.975131i | \(-0.428863\pi\) | ||||
0.221629 | + | 0.975131i | \(0.428863\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −25.0243 | − | 43.3433i | −0.799780 | − | 1.38526i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −3.97938 | + | 6.89249i | −0.126923 | + | 0.219836i | −0.922483 | − | 0.386038i | \(-0.873843\pi\) |
0.795560 | + | 0.605874i | \(0.207177\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 25.0591 | + | 43.4036i | 0.798449 | + | 1.38296i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 14.3355 | − | 24.8298i | 0.455842 | − | 0.789542i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.36428 | − | 7.55916i | −0.138636 | − | 0.240125i | 0.788345 | − | 0.615234i | \(-0.210938\pi\) |
−0.926981 | + | 0.375109i | \(0.877605\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.13391 | − | 5.42809i | 0.0993515 | − | 0.172082i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.15190 | − | 1.99514i | 0.0364810 | − | 0.0631869i | −0.847208 | − | 0.531261i | \(-0.821719\pi\) |
0.883689 | + | 0.468074i | \(0.155052\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 3024.2.q.k.2305.2 | 22 | ||
3.2 | odd | 2 | 1008.2.q.k.625.10 | 22 | |||
4.3 | odd | 2 | 1512.2.q.c.793.2 | 22 | |||
7.4 | even | 3 | 3024.2.t.l.1873.10 | 22 | |||
9.2 | odd | 6 | 1008.2.t.k.961.7 | 22 | |||
9.7 | even | 3 | 3024.2.t.l.289.10 | 22 | |||
12.11 | even | 2 | 504.2.q.d.121.2 | yes | 22 | ||
21.11 | odd | 6 | 1008.2.t.k.193.7 | 22 | |||
28.11 | odd | 6 | 1512.2.t.d.361.10 | 22 | |||
36.7 | odd | 6 | 1512.2.t.d.289.10 | 22 | |||
36.11 | even | 6 | 504.2.t.d.457.5 | yes | 22 | ||
63.11 | odd | 6 | 1008.2.q.k.529.10 | 22 | |||
63.25 | even | 3 | inner | 3024.2.q.k.2881.2 | 22 | ||
84.11 | even | 6 | 504.2.t.d.193.5 | yes | 22 | ||
252.11 | even | 6 | 504.2.q.d.25.2 | ✓ | 22 | ||
252.151 | odd | 6 | 1512.2.q.c.1369.2 | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.q.d.25.2 | ✓ | 22 | 252.11 | even | 6 | ||
504.2.q.d.121.2 | yes | 22 | 12.11 | even | 2 | ||
504.2.t.d.193.5 | yes | 22 | 84.11 | even | 6 | ||
504.2.t.d.457.5 | yes | 22 | 36.11 | even | 6 | ||
1008.2.q.k.529.10 | 22 | 63.11 | odd | 6 | |||
1008.2.q.k.625.10 | 22 | 3.2 | odd | 2 | |||
1008.2.t.k.193.7 | 22 | 21.11 | odd | 6 | |||
1008.2.t.k.961.7 | 22 | 9.2 | odd | 6 | |||
1512.2.q.c.793.2 | 22 | 4.3 | odd | 2 | |||
1512.2.q.c.1369.2 | 22 | 252.151 | odd | 6 | |||
1512.2.t.d.289.10 | 22 | 36.7 | odd | 6 | |||
1512.2.t.d.361.10 | 22 | 28.11 | odd | 6 | |||
3024.2.q.k.2305.2 | 22 | 1.1 | even | 1 | trivial | ||
3024.2.q.k.2881.2 | 22 | 63.25 | even | 3 | inner | ||
3024.2.t.l.289.10 | 22 | 9.7 | even | 3 | |||
3024.2.t.l.1873.10 | 22 | 7.4 | even | 3 |