Properties

Label 2736.2.dc.d.1889.4
Level $2736$
Weight $2$
Character 2736.1889
Analytic conductor $21.847$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [2736,2,Mod(449,2736)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2736, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 3, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2736.449");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2736.dc (of order \(6\), 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: \(21.8470699930\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} + 10x^{14} + 46x^{12} + 126x^{10} + 315x^{8} + 1134x^{6} + 3726x^{4} + 7290x^{2} + 6561 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 2^{2}\cdot 3^{7} \)
Twist minimal: no (minimal twist has level 684)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 1889.4
Root \(-0.654543 + 1.60361i\) of defining polynomial
Character \(\chi\) \(=\) 2736.1889
Dual form 2736.2.dc.d.449.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.406956 - 0.234956i) q^{5} +3.49289 q^{7} +O(q^{10})\) \(q+(-0.406956 - 0.234956i) q^{5} +3.49289 q^{7} -1.34919i q^{11} +(4.30672 - 2.48649i) q^{13} +(-6.31655 - 3.64686i) q^{17} +(-1.88959 + 3.92803i) q^{19} +(6.97653 - 4.02790i) q^{23} +(-2.38959 - 4.13889i) q^{25} +(-4.74117 - 8.21194i) q^{29} +3.95998i q^{31} +(-1.42145 - 0.820674i) q^{35} +0.581007i q^{37} +(-0.761473 + 1.31891i) q^{41} +(4.63603 - 8.02985i) q^{43} +(1.06693 - 0.615993i) q^{47} +5.20026 q^{49} +(5.09568 + 8.82598i) q^{53} +(-0.316999 + 0.549059i) q^{55} +(-5.09568 + 8.82598i) q^{59} +(-3.59618 - 6.22877i) q^{61} -2.33686 q^{65} +(-9.23616 + 5.33250i) q^{67} +(3.67423 - 6.36396i) q^{71} +(-0.703424 + 1.21837i) q^{73} -4.71255i q^{77} +(1.56422 + 0.903104i) q^{79} -5.53518i q^{83} +(1.71370 + 2.96822i) q^{85} +(-7.73800 - 13.4026i) q^{89} +(15.0429 - 8.68501i) q^{91} +(1.69189 - 1.15456i) q^{95} +(9.66561 + 5.58044i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 12 q^{19} + 4 q^{25} + 4 q^{43} - 20 q^{55} + 12 q^{61} - 36 q^{67} + 44 q^{73} + 12 q^{79} + 56 q^{85} + 60 q^{91}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2736\mathbb{Z}\right)^\times\).

\(n\) \(1009\) \(1217\) \(1711\) \(2053\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(-1\) \(1\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) −0.406956 0.234956i −0.181996 0.105075i 0.406234 0.913769i \(-0.366842\pi\)
−0.588230 + 0.808694i \(0.700175\pi\)
\(6\) 0 0
\(7\) 3.49289 1.32019 0.660094 0.751183i \(-0.270517\pi\)
0.660094 + 0.751183i \(0.270517\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 1.34919i 0.406795i −0.979096 0.203397i \(-0.934802\pi\)
0.979096 0.203397i \(-0.0651983\pi\)
\(12\) 0 0
\(13\) 4.30672 2.48649i 1.19447 0.689627i 0.235152 0.971959i \(-0.424441\pi\)
0.959317 + 0.282332i \(0.0911078\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −6.31655 3.64686i −1.53199 0.884494i −0.999270 0.0382017i \(-0.987837\pi\)
−0.532719 0.846292i \(-0.678830\pi\)
\(18\) 0 0
\(19\) −1.88959 + 3.92803i −0.433502 + 0.901153i
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 6.97653 4.02790i 1.45471 0.839875i 0.455964 0.889998i \(-0.349295\pi\)
0.998743 + 0.0501233i \(0.0159614\pi\)
\(24\) 0 0
\(25\) −2.38959 4.13889i −0.477918 0.827779i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −4.74117 8.21194i −0.880413 1.52492i −0.850883 0.525355i \(-0.823932\pi\)
−0.0295296 0.999564i \(-0.509401\pi\)
\(30\) 0 0
\(31\) 3.95998i 0.711234i 0.934632 + 0.355617i \(0.115729\pi\)
−0.934632 + 0.355617i \(0.884271\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −1.42145 0.820674i −0.240269 0.138719i
\(36\) 0 0
\(37\) 0.581007i 0.0955169i 0.998859 + 0.0477584i \(0.0152078\pi\)
−0.998859 + 0.0477584i \(0.984792\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −0.761473 + 1.31891i −0.118922 + 0.205979i −0.919341 0.393462i \(-0.871277\pi\)
0.800419 + 0.599441i \(0.204611\pi\)
\(42\) 0 0
\(43\) 4.63603 8.02985i 0.706989 1.22454i −0.258980 0.965883i \(-0.583386\pi\)
0.965969 0.258658i \(-0.0832802\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 1.06693 0.615993i 0.155628 0.0898519i −0.420164 0.907448i \(-0.638027\pi\)
0.575792 + 0.817597i \(0.304694\pi\)
\(48\) 0 0
\(49\) 5.20026 0.742894
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 5.09568 + 8.82598i 0.699946 + 1.21234i 0.968485 + 0.249073i \(0.0801260\pi\)
−0.268539 + 0.963269i \(0.586541\pi\)
\(54\) 0 0
\(55\) −0.316999 + 0.549059i −0.0427442 + 0.0740350i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −5.09568 + 8.82598i −0.663402 + 1.14905i 0.316314 + 0.948654i \(0.397555\pi\)
−0.979716 + 0.200391i \(0.935779\pi\)
\(60\) 0 0
\(61\) −3.59618 6.22877i −0.460444 0.797512i 0.538539 0.842601i \(-0.318976\pi\)
−0.998983 + 0.0450883i \(0.985643\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −2.33686 −0.289852
\(66\) 0 0
\(67\) −9.23616 + 5.33250i −1.12838 + 0.651469i −0.943526 0.331298i \(-0.892514\pi\)
−0.184851 + 0.982767i \(0.559180\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 3.67423 6.36396i 0.436051 0.755263i −0.561329 0.827592i \(-0.689710\pi\)
0.997381 + 0.0723293i \(0.0230432\pi\)
\(72\) 0 0
\(73\) −0.703424 + 1.21837i −0.0823296 + 0.142599i −0.904250 0.427003i \(-0.859569\pi\)
0.821921 + 0.569602i \(0.192903\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 4.71255i 0.537045i
\(78\) 0 0
\(79\) 1.56422 + 0.903104i 0.175989 + 0.101607i 0.585407 0.810740i \(-0.300935\pi\)
−0.409418 + 0.912347i \(0.634268\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 5.53518i 0.607565i −0.952741 0.303782i \(-0.901750\pi\)
0.952741 0.303782i \(-0.0982496\pi\)
\(84\) 0 0
\(85\) 1.71370 + 2.96822i 0.185877 + 0.321949i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −7.73800 13.4026i −0.820226 1.42067i −0.905513 0.424317i \(-0.860514\pi\)
0.0852870 0.996356i \(-0.472819\pi\)
\(90\) 0 0
\(91\) 15.0429 8.68501i 1.57692 0.910437i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 1.69189 1.15456i 0.173585 0.118456i
\(96\) 0 0
\(97\) 9.66561 + 5.58044i 0.981394 + 0.566608i 0.902691 0.430290i \(-0.141589\pi\)
0.0787031 + 0.996898i \(0.474922\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −5.75566 + 3.32303i −0.572710 + 0.330654i −0.758231 0.651986i \(-0.773936\pi\)
0.185521 + 0.982640i \(0.440603\pi\)
\(102\) 0 0
\(103\) 4.89881i 0.482694i 0.970439 + 0.241347i \(0.0775893\pi\)
−0.970439 + 0.241347i \(0.922411\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −5.28463 −0.510885 −0.255442 0.966824i \(-0.582221\pi\)
−0.255442 + 0.966824i \(0.582221\pi\)
\(108\) 0 0
\(109\) −4.19011 2.41916i −0.401340 0.231714i 0.285722 0.958313i \(-0.407767\pi\)
−0.687062 + 0.726599i \(0.741100\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 20.7955 1.95627 0.978137 0.207960i \(-0.0666825\pi\)
0.978137 + 0.207960i \(0.0666825\pi\)
\(114\) 0 0
\(115\) −3.78552 −0.353001
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −22.0630 12.7381i −2.02251 1.16770i
\(120\) 0 0
\(121\) 9.17970 0.834518
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 4.59535i 0.411021i
\(126\) 0 0
\(127\) 12.6103 7.28054i 1.11898 0.646044i 0.177840 0.984059i \(-0.443089\pi\)
0.941141 + 0.338016i \(0.109756\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −1.06693 0.615993i −0.0932183 0.0538196i 0.452666 0.891680i \(-0.350473\pi\)
−0.545884 + 0.837860i \(0.683806\pi\)
\(132\) 0 0
\(133\) −6.60013 + 13.7202i −0.572304 + 1.18969i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 13.1566 7.59595i 1.12404 0.648966i 0.181612 0.983370i \(-0.441869\pi\)
0.942430 + 0.334405i \(0.108535\pi\)
\(138\) 0 0
\(139\) −4.34657 7.52848i −0.368671 0.638558i 0.620687 0.784059i \(-0.286854\pi\)
−0.989358 + 0.145501i \(0.953521\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −3.35473 5.81056i −0.280537 0.485904i
\(144\) 0 0
\(145\) 4.45586i 0.370039i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −12.1911 7.03855i −0.998737 0.576621i −0.0908623 0.995863i \(-0.528962\pi\)
−0.907874 + 0.419243i \(0.862296\pi\)
\(150\) 0 0
\(151\) 14.4128i 1.17289i −0.809987 0.586447i \(-0.800526\pi\)
0.809987 0.586447i \(-0.199474\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0.930421 1.61154i 0.0747332 0.129442i
\(156\) 0 0
\(157\) 2.27918 3.94766i 0.181899 0.315058i −0.760628 0.649187i \(-0.775109\pi\)
0.942527 + 0.334130i \(0.108442\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 24.3682 14.0690i 1.92048 1.10879i
\(162\) 0 0
\(163\) 20.3066 1.59053 0.795267 0.606259i \(-0.207331\pi\)
0.795267 + 0.606259i \(0.207331\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −7.75542 13.4328i −0.600133 1.03946i −0.992800 0.119780i \(-0.961781\pi\)
0.392668 0.919680i \(-0.371552\pi\)
\(168\) 0 0
\(169\) 5.86522 10.1589i 0.451171 0.781451i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −0.813911 + 1.40974i −0.0618805 + 0.107180i −0.895306 0.445452i \(-0.853043\pi\)
0.833425 + 0.552632i \(0.186376\pi\)
\(174\) 0 0
\(175\) −8.34657 14.4567i −0.630942 1.09282i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 10.8023 0.807401 0.403700 0.914891i \(-0.367724\pi\)
0.403700 + 0.914891i \(0.367724\pi\)
\(180\) 0 0
\(181\) 3.19328 1.84364i 0.237355 0.137037i −0.376606 0.926374i \(-0.622909\pi\)
0.613960 + 0.789337i \(0.289575\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0.136511 0.236444i 0.0100365 0.0173837i
\(186\) 0 0
\(187\) −4.92029 + 8.52220i −0.359808 + 0.623205i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 18.2996i 1.32411i 0.749453 + 0.662057i \(0.230316\pi\)
−0.749453 + 0.662057i \(0.769684\pi\)
\(192\) 0 0
\(193\) −6.17194 3.56337i −0.444266 0.256497i 0.261139 0.965301i \(-0.415902\pi\)
−0.705406 + 0.708804i \(0.749235\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 5.88677i 0.419415i 0.977764 + 0.209708i \(0.0672512\pi\)
−0.977764 + 0.209708i \(0.932749\pi\)
\(198\) 0 0
\(199\) −1.22602 2.12353i −0.0869103 0.150533i 0.819293 0.573375i \(-0.194366\pi\)
−0.906204 + 0.422842i \(0.861033\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −16.5604 28.6834i −1.16231 2.01318i
\(204\) 0 0
\(205\) 0.619772 0.357825i 0.0432867 0.0249916i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 5.29965 + 2.54941i 0.366584 + 0.176346i
\(210\) 0 0
\(211\) −13.1777 7.60813i −0.907188 0.523765i −0.0276624 0.999617i \(-0.508806\pi\)
−0.879525 + 0.475852i \(0.842140\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −3.77332 + 2.17853i −0.257338 + 0.148574i
\(216\) 0 0
\(217\) 13.8318i 0.938961i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −36.2715 −2.43988
\(222\) 0 0
\(223\) 21.1808 + 12.2288i 1.41837 + 0.818898i 0.996156 0.0875966i \(-0.0279186\pi\)
0.422217 + 0.906495i \(0.361252\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 2.84290 0.188690 0.0943449 0.995540i \(-0.469924\pi\)
0.0943449 + 0.995540i \(0.469924\pi\)
\(228\) 0 0
\(229\) 6.64189 0.438909 0.219454 0.975623i \(-0.429572\pi\)
0.219454 + 0.975623i \(0.429572\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −3.14836 1.81771i −0.206256 0.119082i 0.393314 0.919404i \(-0.371328\pi\)
−0.599570 + 0.800322i \(0.704662\pi\)
\(234\) 0 0
\(235\) −0.578925 −0.0377649
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 0.762075i 0.0492945i −0.999696 0.0246473i \(-0.992154\pi\)
0.999696 0.0246473i \(-0.00784626\pi\)
\(240\) 0 0
\(241\) 6.97549 4.02730i 0.449331 0.259421i −0.258217 0.966087i \(-0.583135\pi\)
0.707548 + 0.706666i \(0.249801\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −2.11627 1.22183i −0.135204 0.0780599i
\(246\) 0 0
\(247\) 1.62906 + 21.6154i 0.103654 + 1.37535i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −21.2665 + 12.2782i −1.34233 + 0.774995i −0.987149 0.159803i \(-0.948914\pi\)
−0.355181 + 0.934797i \(0.615581\pi\)
\(252\) 0 0
\(253\) −5.43438 9.41263i −0.341657 0.591767i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −9.33081 16.1614i −0.582040 1.00812i −0.995237 0.0974812i \(-0.968921\pi\)
0.413197 0.910641i \(-0.364412\pi\)
\(258\) 0 0
\(259\) 2.02939i 0.126100i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 18.9821 + 10.9593i 1.17049 + 0.675780i 0.953794 0.300460i \(-0.0971401\pi\)
0.216691 + 0.976240i \(0.430473\pi\)
\(264\) 0 0
\(265\) 4.78904i 0.294189i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −6.97653 + 12.0837i −0.425366 + 0.736756i −0.996455 0.0841325i \(-0.973188\pi\)
0.571088 + 0.820889i \(0.306521\pi\)
\(270\) 0 0
\(271\) 1.00000 1.73205i 0.0607457 0.105215i −0.834053 0.551684i \(-0.813985\pi\)
0.894799 + 0.446469i \(0.147319\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −5.58414 + 3.22400i −0.336736 + 0.194415i
\(276\) 0 0
\(277\) −8.35811 −0.502190 −0.251095 0.967962i \(-0.580791\pi\)
−0.251095 + 0.967962i \(0.580791\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −4.87768 8.44839i −0.290978 0.503988i 0.683063 0.730359i \(-0.260647\pi\)
−0.974041 + 0.226371i \(0.927314\pi\)
\(282\) 0 0
\(283\) 4.41318 7.64385i 0.262336 0.454380i −0.704526 0.709678i \(-0.748840\pi\)
0.966862 + 0.255298i \(0.0821737\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −2.65974 + 4.60681i −0.157000 + 0.271931i
\(288\) 0 0
\(289\) 18.0992 + 31.3488i 1.06466 + 1.84404i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 19.3358 1.12961 0.564805 0.825224i \(-0.308951\pi\)
0.564805 + 0.825224i \(0.308951\pi\)
\(294\) 0 0
\(295\) 4.14743 2.39452i 0.241473 0.139414i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 20.0306 34.6941i 1.15840 2.00641i
\(300\) 0 0
\(301\) 16.1931 28.0473i 0.933357 1.61662i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 3.37978i 0.193525i
\(306\) 0 0
\(307\) 8.04900 + 4.64709i 0.459381 + 0.265224i 0.711784 0.702399i \(-0.247888\pi\)
−0.252403 + 0.967622i \(0.581221\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 18.7734i 1.06454i 0.846573 + 0.532272i \(0.178662\pi\)
−0.846573 + 0.532272i \(0.821338\pi\)
\(312\) 0 0
\(313\) 14.5891 + 25.2690i 0.824623 + 1.42829i 0.902207 + 0.431303i \(0.141946\pi\)
−0.0775842 + 0.996986i \(0.524721\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 7.43254 + 12.8735i 0.417453 + 0.723050i 0.995683 0.0928242i \(-0.0295894\pi\)
−0.578229 + 0.815874i \(0.696256\pi\)
\(318\) 0 0
\(319\) −11.0794 + 6.39671i −0.620329 + 0.358147i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 26.2607 17.9205i 1.46118 0.997126i
\(324\) 0 0
\(325\) −20.5826 11.8834i −1.14172 0.659171i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 3.72667 2.15160i 0.205458 0.118621i
\(330\) 0 0
\(331\) 22.5415i 1.23899i 0.784999 + 0.619497i \(0.212664\pi\)
−0.784999 + 0.619497i \(0.787336\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 5.01161 0.273814
\(336\) 0 0
\(337\) −8.17511 4.71990i −0.445326 0.257109i 0.260528 0.965466i \(-0.416103\pi\)
−0.705854 + 0.708357i \(0.749437\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 5.34275 0.289326
\(342\) 0 0
\(343\) −6.28630 −0.339428
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 24.8418 + 14.3424i 1.33358 + 0.769942i 0.985846 0.167651i \(-0.0536183\pi\)
0.347733 + 0.937594i \(0.386952\pi\)
\(348\) 0 0
\(349\) −33.1576 −1.77488 −0.887442 0.460919i \(-0.847520\pi\)
−0.887442 + 0.460919i \(0.847520\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 0.993688i 0.0528887i −0.999650 0.0264443i \(-0.991582\pi\)
0.999650 0.0264443i \(-0.00841848\pi\)
\(354\) 0 0
\(355\) −2.99050 + 1.72657i −0.158719 + 0.0916366i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 15.8513 + 9.15177i 0.836601 + 0.483012i 0.856107 0.516798i \(-0.172876\pi\)
−0.0195066 + 0.999810i \(0.506210\pi\)
\(360\) 0 0
\(361\) −11.8589 14.8448i −0.624152 0.781303i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 0.572525 0.330547i 0.0299673 0.0173016i
\(366\) 0 0
\(367\) −10.0460 17.4003i −0.524400 0.908287i −0.999596 0.0284071i \(-0.990957\pi\)
0.475197 0.879879i \(-0.342377\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 17.7986 + 30.8282i 0.924060 + 1.60052i
\(372\) 0 0
\(373\) 32.6611i 1.69113i −0.533873 0.845565i \(-0.679264\pi\)
0.533873 0.845565i \(-0.320736\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −40.8377 23.5777i −2.10325 1.21431i
\(378\) 0 0
\(379\) 16.9346i 0.869874i 0.900461 + 0.434937i \(0.143229\pi\)
−0.900461 + 0.434937i \(0.856771\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −0.912997 + 1.58136i −0.0466520 + 0.0808036i −0.888408 0.459054i \(-0.848189\pi\)
0.841756 + 0.539857i \(0.181522\pi\)
\(384\) 0 0
\(385\) −1.10724 + 1.91780i −0.0564303 + 0.0977401i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 0.336928 0.194525i 0.0170829 0.00986283i −0.491434 0.870915i \(-0.663527\pi\)
0.508517 + 0.861052i \(0.330194\pi\)
\(390\) 0 0
\(391\) −58.7568 −2.97146
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −0.424379 0.735047i −0.0213528 0.0369842i
\(396\) 0 0
\(397\) 10.4415 18.0852i 0.524044 0.907670i −0.475564 0.879681i \(-0.657756\pi\)
0.999608 0.0279895i \(-0.00891051\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −6.11018 + 10.5831i −0.305128 + 0.528497i −0.977290 0.211907i \(-0.932033\pi\)
0.672162 + 0.740404i \(0.265366\pi\)
\(402\) 0 0
\(403\) 9.84644 + 17.0545i 0.490486 + 0.849547i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0.783886 0.0388558
\(408\) 0 0
\(409\) 16.4233 9.48201i 0.812081 0.468855i −0.0355969 0.999366i \(-0.511333\pi\)
0.847678 + 0.530511i \(0.178000\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −17.7986 + 30.8282i −0.875814 + 1.51695i
\(414\) 0 0
\(415\) −1.30052 + 2.25257i −0.0638401 + 0.110574i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 15.3264i 0.748745i 0.927278 + 0.374373i \(0.122142\pi\)
−0.927278 + 0.374373i \(0.877858\pi\)
\(420\) 0 0
\(421\) 10.6624 + 6.15596i 0.519656 + 0.300023i 0.736794 0.676118i \(-0.236339\pi\)
−0.217138 + 0.976141i \(0.569672\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 34.8580i 1.69086i
\(426\) 0 0
\(427\) −12.5611 21.7564i −0.607872 1.05287i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 2.69475 + 4.66745i 0.129802 + 0.224823i 0.923600 0.383358i \(-0.125233\pi\)
−0.793798 + 0.608182i \(0.791899\pi\)
\(432\) 0 0
\(433\) −28.5304 + 16.4721i −1.37108 + 0.791596i −0.991065 0.133382i \(-0.957416\pi\)
−0.380020 + 0.924978i \(0.624083\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 2.63894 + 35.0151i 0.126238 + 1.67500i
\(438\) 0 0
\(439\) 30.6658 + 17.7049i 1.46360 + 0.845009i 0.999175 0.0406035i \(-0.0129281\pi\)
0.464424 + 0.885613i \(0.346261\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −20.4202 + 11.7896i −0.970191 + 0.560140i −0.899295 0.437344i \(-0.855919\pi\)
−0.0708967 + 0.997484i \(0.522586\pi\)
\(444\) 0 0
\(445\) 7.27236i 0.344743i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 27.9061 1.31697 0.658485 0.752594i \(-0.271197\pi\)
0.658485 + 0.752594i \(0.271197\pi\)
\(450\) 0 0
\(451\) 1.77946 + 1.02737i 0.0837913 + 0.0483769i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −8.16238 −0.382658
\(456\) 0 0
\(457\) 1.38023 0.0645644 0.0322822 0.999479i \(-0.489722\pi\)
0.0322822 + 0.999479i \(0.489722\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −8.29648 4.78998i −0.386406 0.223091i 0.294196 0.955745i \(-0.404948\pi\)
−0.680602 + 0.732654i \(0.738281\pi\)
\(462\) 0 0
\(463\) −17.3114 −0.804527 −0.402263 0.915524i \(-0.631776\pi\)
−0.402263 + 0.915524i \(0.631776\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 14.7691i 0.683432i 0.939803 + 0.341716i \(0.111008\pi\)
−0.939803 + 0.341716i \(0.888992\pi\)
\(468\) 0 0
\(469\) −32.2609 + 18.6258i −1.48967 + 0.860061i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −10.8338 6.25487i −0.498137 0.287599i
\(474\) 0 0
\(475\) 20.7731 1.56558i 0.953134 0.0718336i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −27.8909 + 16.1028i −1.27437 + 0.735757i −0.975807 0.218633i \(-0.929840\pi\)
−0.298562 + 0.954390i \(0.596507\pi\)
\(480\) 0 0
\(481\) 1.44466 + 2.50223i 0.0658710 + 0.114092i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −2.62232 4.54198i −0.119073 0.206241i
\(486\) 0 0
\(487\) 5.60690i 0.254073i 0.991898 + 0.127037i \(0.0405466\pi\)
−0.991898 + 0.127037i \(0.959453\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 3.87723 + 2.23852i 0.174977 + 0.101023i 0.584930 0.811083i \(-0.301122\pi\)
−0.409954 + 0.912106i \(0.634455\pi\)
\(492\) 0 0
\(493\) 69.1615i 3.11488i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 12.8337 22.2286i 0.575669 0.997089i
\(498\) 0 0
\(499\) 6.05013 10.4791i 0.270841 0.469111i −0.698236 0.715867i \(-0.746032\pi\)
0.969077 + 0.246757i \(0.0793649\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −14.4265 + 8.32914i −0.643246 + 0.371378i −0.785864 0.618400i \(-0.787781\pi\)
0.142618 + 0.989778i \(0.454448\pi\)
\(504\) 0 0
\(505\) 3.12306 0.138975
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 11.5662 + 20.0332i 0.512661 + 0.887956i 0.999892 + 0.0146825i \(0.00467374\pi\)
−0.487231 + 0.873273i \(0.661993\pi\)
\(510\) 0 0
\(511\) −2.45698 + 4.25562i −0.108690 + 0.188257i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 1.15101 1.99360i 0.0507193 0.0878485i
\(516\) 0 0
\(517\) −0.831089 1.43949i −0.0365513 0.0633087i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 28.3189 1.24067 0.620336 0.784336i \(-0.286996\pi\)
0.620336 + 0.784336i \(0.286996\pi\)
\(522\) 0 0
\(523\) −21.2457 + 12.2662i −0.929008 + 0.536363i −0.886498 0.462733i \(-0.846869\pi\)
−0.0425103 + 0.999096i \(0.513536\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 14.4415 25.0134i 0.629082 1.08960i
\(528\) 0 0
\(529\) 20.9480 36.2829i 0.910781 1.57752i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 7.57357i 0.328048i
\(534\) 0 0
\(535\) 2.15061 + 1.24166i 0.0929790 + 0.0536815i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 7.01611i 0.302205i
\(540\) 0 0
\(541\) −8.97233 15.5405i −0.385750 0.668139i 0.606123 0.795371i \(-0.292724\pi\)
−0.991873 + 0.127232i \(0.959391\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 1.13679 + 1.96898i 0.0486949 + 0.0843420i
\(546\) 0 0
\(547\) −9.51521 + 5.49361i −0.406841 + 0.234890i −0.689432 0.724351i \(-0.742140\pi\)
0.282591 + 0.959241i \(0.408806\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 41.2156 3.10625i 1.75585 0.132330i
\(552\) 0 0
\(553\) 5.46365 + 3.15444i 0.232338 + 0.134141i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −3.00262 + 1.73357i −0.127225 + 0.0734535i −0.562262 0.826959i \(-0.690069\pi\)
0.435037 + 0.900413i \(0.356735\pi\)
\(558\) 0 0
\(559\) 46.1097i 1.95023i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 1.55779 0.0656532 0.0328266 0.999461i \(-0.489549\pi\)
0.0328266 + 0.999461i \(0.489549\pi\)
\(564\) 0 0
\(565\) −8.46284 4.88602i −0.356034 0.205556i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 18.3886 0.770890 0.385445 0.922731i \(-0.374048\pi\)
0.385445 + 0.922731i \(0.374048\pi\)
\(570\) 0 0
\(571\) −28.4660 −1.19126 −0.595632 0.803257i \(-0.703098\pi\)
−0.595632 + 0.803257i \(0.703098\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −33.3421 19.2501i −1.39046 0.802783i
\(576\) 0 0
\(577\) −18.6213 −0.775216 −0.387608 0.921824i \(-0.626699\pi\)
−0.387608 + 0.921824i \(0.626699\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 19.3337i 0.802099i
\(582\) 0 0
\(583\) 11.9079 6.87502i 0.493174 0.284734i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −5.35787 3.09337i −0.221143 0.127677i 0.385336 0.922776i \(-0.374085\pi\)
−0.606479 + 0.795099i \(0.707419\pi\)
\(588\) 0 0
\(589\) −15.5549 7.48275i −0.640930 0.308321i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 16.5420 9.55051i 0.679297 0.392192i −0.120293 0.992738i \(-0.538383\pi\)
0.799590 + 0.600546i \(0.205050\pi\)
\(594\) 0 0
\(595\) 5.98577 + 10.3677i 0.245393 + 0.425033i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 21.9789 + 38.0686i 0.898035 + 1.55544i 0.830003 + 0.557758i \(0.188338\pi\)
0.0680310 + 0.997683i \(0.478328\pi\)
\(600\) 0 0
\(601\) 25.3002i 1.03202i 0.856583 + 0.516009i \(0.172583\pi\)
−0.856583 + 0.516009i \(0.827417\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −3.73573 2.15682i −0.151879 0.0876874i
\(606\) 0 0
\(607\) 12.2880i 0.498754i 0.968406 + 0.249377i \(0.0802259\pi\)
−0.968406 + 0.249377i \(0.919774\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 3.06332 5.30582i 0.123929 0.214651i
\(612\) 0 0
\(613\) 5.52042 9.56165i 0.222968 0.386192i −0.732740 0.680509i \(-0.761759\pi\)
0.955708 + 0.294317i \(0.0950922\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 27.4315 15.8376i 1.10435 0.637598i 0.166991 0.985958i \(-0.446595\pi\)
0.937361 + 0.348360i \(0.113261\pi\)
\(618\) 0 0
\(619\) 34.0244 1.36755 0.683777 0.729691i \(-0.260336\pi\)
0.683777 + 0.729691i \(0.260336\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −27.0280 46.8138i −1.08285 1.87556i
\(624\) 0 0
\(625\) −10.8683 + 18.8244i −0.434730 + 0.752975i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 2.11885 3.66996i 0.0844841 0.146331i
\(630\) 0 0
\(631\) −13.9530 24.1674i −0.555462 0.962088i −0.997867 0.0652727i \(-0.979208\pi\)
0.442406 0.896815i \(-0.354125\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −6.84243 −0.271533
\(636\) 0 0
\(637\) 22.3961 12.9304i 0.887364 0.512320i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 0.0350138 0.0606458i 0.00138296 0.00239536i −0.865333 0.501197i \(-0.832893\pi\)
0.866716 + 0.498802i \(0.166226\pi\)
\(642\) 0 0
\(643\) 16.0562 27.8101i 0.633194 1.09672i −0.353700 0.935359i \(-0.615077\pi\)
0.986895 0.161366i \(-0.0515900\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 5.51784i 0.216929i 0.994100 + 0.108464i \(0.0345933\pi\)
−0.994100 + 0.108464i \(0.965407\pi\)
\(648\) 0 0
\(649\) 11.9079 + 6.87502i 0.467426 + 0.269868i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 24.9898i 0.977928i 0.872304 + 0.488964i \(0.162625\pi\)
−0.872304 + 0.488964i \(0.837375\pi\)
\(654\) 0 0
\(655\) 0.289463 + 0.501364i 0.0113102 + 0.0195899i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −1.43887 2.49220i −0.0560506 0.0970824i 0.836639 0.547755i \(-0.184517\pi\)
−0.892689 + 0.450673i \(0.851184\pi\)
\(660\) 0 0
\(661\) −28.9510 + 16.7149i −1.12606 + 0.650133i −0.942942 0.332958i \(-0.891953\pi\)
−0.183121 + 0.983090i \(0.558620\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 5.90960 4.03276i 0.229164 0.156384i
\(666\) 0 0
\(667\) −66.1538 38.1939i −2.56148 1.47887i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −8.40377 + 4.85192i −0.324424 + 0.187306i
\(672\) 0 0
\(673\) 1.66815i 0.0643026i −0.999483 0.0321513i \(-0.989764\pi\)
0.999483 0.0321513i \(-0.0102358\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −4.30258 −0.165361 −0.0826807 0.996576i \(-0.526348\pi\)
−0.0826807 + 0.996576i \(0.526348\pi\)
\(678\) 0 0
\(679\) 33.7609 + 19.4918i 1.29562 + 0.748029i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 0.412745 0.0157933 0.00789663 0.999969i \(-0.497486\pi\)
0.00789663 + 0.999969i \(0.497486\pi\)
\(684\) 0 0
\(685\) −7.13885 −0.272762
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 43.8914 + 25.3407i 1.67213 + 0.965403i
\(690\) 0 0
\(691\) 12.9573 0.492920 0.246460 0.969153i \(-0.420733\pi\)
0.246460 + 0.969153i \(0.420733\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 4.08501i 0.154953i
\(696\) 0 0
\(697\) 9.61977 5.55398i 0.364375 0.210372i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −16.1208 9.30735i −0.608874 0.351534i 0.163651 0.986518i \(-0.447673\pi\)
−0.772525 + 0.634985i \(0.781006\pi\)
\(702\) 0 0
\(703\) −2.28221 1.09787i −0.0860753 0.0414068i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −20.1039 + 11.6070i −0.756084 + 0.436525i
\(708\) 0 0
\(709\) 17.7822 + 30.7997i 0.667825 + 1.15671i 0.978511 + 0.206194i \(0.0661079\pi\)
−0.310686 + 0.950513i \(0.600559\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 15.9504 + 27.6269i 0.597347 + 1.03464i
\(714\) 0 0
\(715\) 3.15286i 0.117910i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −10.6858 6.16944i −0.398512 0.230081i 0.287330 0.957832i \(-0.407232\pi\)
−0.685842 + 0.727751i \(0.740566\pi\)
\(720\) 0 0
\(721\) 17.1110i 0.637247i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −22.6589 + 39.2464i −0.841530 + 1.45757i
\(726\) 0 0
\(727\) −5.42944 + 9.40407i −0.201367 + 0.348778i −0.948969 0.315369i \(-0.897872\pi\)
0.747602 + 0.664147i \(0.231205\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −58.5675 + 33.8140i −2.16620 + 1.25065i
\(732\) 0 0
\(733\) −28.5581 −1.05482 −0.527409 0.849612i \(-0.676836\pi\)
−0.527409 + 0.849612i \(0.676836\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 7.19453 + 12.4613i 0.265014 + 0.459018i
\(738\) 0 0
\(739\) −18.0090 + 31.1925i −0.662472 + 1.14744i 0.317492 + 0.948261i \(0.397159\pi\)
−0.979964 + 0.199175i \(0.936174\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −7.65055 + 13.2511i −0.280671 + 0.486137i −0.971550 0.236833i \(-0.923890\pi\)
0.690879 + 0.722971i \(0.257224\pi\)
\(744\) 0 0
\(745\) 3.30750 + 5.72876i 0.121177 + 0.209885i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −18.4586 −0.674463
\(750\) 0 0
\(751\) −1.48161 + 0.855410i −0.0540648 + 0.0312143i −0.526789 0.849996i \(-0.676604\pi\)
0.472724 + 0.881211i \(0.343271\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −3.38637 + 5.86536i −0.123242 + 0.213462i
\(756\) 0 0
\(757\) 6.74519 11.6830i 0.245158 0.424626i −0.717018 0.697055i \(-0.754493\pi\)
0.962176 + 0.272429i \(0.0878268\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 32.3374i 1.17223i −0.810228 0.586115i \(-0.800657\pi\)
0.810228 0.586115i \(-0.199343\pi\)
\(762\) 0 0
\(763\) −14.6356 8.44986i −0.529844 0.305906i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 50.6814i 1.83000i
\(768\) 0 0
\(769\) 8.87233 + 15.3673i 0.319945 + 0.554160i 0.980476 0.196638i \(-0.0630024\pi\)
−0.660532 + 0.750798i \(0.729669\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 22.4209 + 38.8341i 0.806424 + 1.39677i 0.915326 + 0.402714i \(0.131933\pi\)
−0.108902 + 0.994052i \(0.534734\pi\)
\(774\) 0 0
\(775\) 16.3899 9.46274i 0.588744 0.339912i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −3.74185 5.48330i −0.134066 0.196459i
\(780\) 0 0
\(781\) −8.58616 4.95722i −0.307237 0.177383i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −1.85505 + 1.07102i −0.0662097 + 0.0382262i
\(786\) 0 0
\(787\) 2.31647i 0.0825731i −0.999147 0.0412866i \(-0.986854\pi\)
0.999147 0.0412866i \(-0.0131457\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 72.6363 2.58265
\(792\) 0 0
\(793\) −30.9755 17.8837i −1.09997 0.635069i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 47.2067 1.67215 0.836074 0.548616i \(-0.184845\pi\)
0.836074 + 0.548616i \(0.184845\pi\)
\(798\) 0 0
\(799\) −8.98577 −0.317894
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 1.64380 + 0.949050i 0.0580085 + 0.0334912i
\(804\) 0 0
\(805\) −13.2224 −0.466028
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 26.6610i 0.937352i 0.883370 + 0.468676i \(0.155269\pi\)
−0.883370 + 0.468676i \(0.844731\pi\)
\(810\) 0 0
\(811\) −11.9478 + 6.89808i −0.419545 + 0.242224i −0.694883 0.719123i \(-0.744544\pi\)
0.275338 + 0.961348i \(0.411210\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −8.26388 4.77115i −0.289471 0.167126i
\(816\) 0 0
\(817\) 22.7813 + 33.3836i 0.797017 + 1.16795i
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −41.3464 + 23.8713i −1.44300 + 0.833115i −0.998049 0.0624403i \(-0.980112\pi\)
−0.444949 + 0.895556i \(0.646778\pi\)
\(822\) 0 0
\(823\) 19.3097 + 33.4455i 0.673096 + 1.16584i 0.977022 + 0.213140i \(0.0683691\pi\)
−0.303926 + 0.952696i \(0.598298\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 21.4671 + 37.1821i 0.746484 + 1.29295i 0.949498 + 0.313772i \(0.101593\pi\)
−0.203014 + 0.979176i \(0.565074\pi\)
\(828\) 0 0
\(829\) 12.0605i 0.418877i 0.977822 + 0.209439i \(0.0671636\pi\)
−0.977822 + 0.209439i \(0.932836\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −32.8477 18.9646i −1.13811 0.657085i
\(834\) 0 0
\(835\) 7.28873i 0.252237i
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 16.4589 28.5076i 0.568223 0.984191i −0.428519 0.903533i \(-0.640964\pi\)
0.996742 0.0806582i \(-0.0257022\pi\)
\(840\) 0 0
\(841\) −30.4573 + 52.7536i −1.05025 + 1.81909i
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −4.77377 + 2.75614i −0.164223 + 0.0948140i
\(846\) 0 0
\(847\) 32.0636 1.10172
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 2.34024 + 4.05341i 0.0802223 + 0.138949i
\(852\) 0 0
\(853\) 18.9818 32.8775i 0.649925 1.12570i −0.333215 0.942851i \(-0.608133\pi\)
0.983140 0.182853i \(-0.0585332\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 17.3194 29.9981i 0.591620 1.02472i −0.402394 0.915466i \(-0.631822\pi\)
0.994014 0.109250i \(-0.0348448\pi\)
\(858\) 0 0
\(859\) −10.7044 18.5406i −0.365230 0.632597i 0.623583 0.781757i \(-0.285676\pi\)
−0.988813 + 0.149160i \(0.952343\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 15.2030 0.517515 0.258758 0.965942i \(-0.416687\pi\)
0.258758 + 0.965942i \(0.416687\pi\)
\(864\) 0 0
\(865\) 0.662451 0.382466i 0.0225240 0.0130043i
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 1.21846 2.11043i 0.0413333 0.0715913i
\(870\) 0 0
\(871\) −26.5184 + 45.9312i −0.898541 + 1.55632i
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 16.0511i 0.542625i
\(876\) 0 0
\(877\) −47.6506 27.5111i −1.60905 0.928983i −0.989584 0.143957i \(-0.954017\pi\)
−0.619462 0.785027i \(-0.712649\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 34.6052i 1.16588i 0.812516 + 0.582939i \(0.198097\pi\)
−0.812516 + 0.582939i \(0.801903\pi\)
\(882\) 0 0
\(883\) −17.1634 29.7279i −0.577596 1.00042i −0.995754 0.0920509i \(-0.970658\pi\)
0.418159 0.908374i \(-0.362676\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 24.0978 + 41.7386i 0.809124 + 1.40144i 0.913471 + 0.406903i \(0.133391\pi\)
−0.104347 + 0.994541i \(0.533275\pi\)
\(888\) 0 0
\(889\) 44.0463 25.4301i 1.47726 0.852899i
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 0.403577 + 5.35492i 0.0135052 + 0.179196i
\(894\) 0 0
\(895\) −4.39605 2.53806i −0.146944 0.0848380i
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 32.5191 18.7749i 1.08457 0.626179i
\(900\) 0 0
\(901\) 74.3330i 2.47639i
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −1.73270 −0.0575968
\(906\) 0 0
\(907\) 14.7241 + 8.50097i 0.488906 + 0.282270i 0.724121 0.689673i \(-0.242246\pi\)
−0.235214 + 0.971943i \(0.575579\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −28.0110 −0.928045 −0.464023 0.885823i \(-0.653594\pi\)
−0.464023 + 0.885823i \(0.653594\pi\)
\(912\) 0 0
\(913\) −7.46798 −0.247154
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −3.72667 2.15160i −0.123066 0.0710519i
\(918\) 0 0
\(919\) −46.1408 −1.52205 −0.761023 0.648725i \(-0.775303\pi\)
−0.761023 + 0.648725i \(0.775303\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 36.5437i 1.20285i
\(924\) 0 0
\(925\) 2.40472 1.38837i 0.0790669 0.0456493i
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −41.6526 24.0482i −1.36658 0.788994i −0.376089 0.926584i \(-0.622731\pi\)
−0.990489 + 0.137589i \(0.956065\pi\)
\(930\) 0 0
\(931\) −9.82636 + 20.4268i −0.322046 + 0.669461i
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 4.00468 2.31210i 0.130967 0.0756139i
\(936\) 0 0
\(937\) −1.17194 2.02986i −0.0382856 0.0663127i 0.846248 0.532790i \(-0.178856\pi\)
−0.884533 + 0.466477i \(0.845523\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 5.24721 + 9.08843i 0.171054 + 0.296274i 0.938789 0.344494i \(-0.111949\pi\)
−0.767735 + 0.640768i \(0.778616\pi\)
\(942\) 0 0
\(943\) 12.2686i 0.399519i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 15.6357 + 9.02729i 0.508093 + 0.293348i 0.732049 0.681252i \(-0.238564\pi\)
−0.223957 + 0.974599i \(0.571897\pi\)
\(948\) 0 0
\(949\) 6.99622i 0.227107i
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 11.1592 19.3283i 0.361482 0.626106i −0.626723 0.779242i \(-0.715604\pi\)
0.988205 + 0.153136i \(0.0489374\pi\)
\(954\) 0 0
\(955\) 4.29961 7.44714i 0.139132 0.240984i
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 45.9544 26.5318i 1.48394 0.856756i
\(960\) 0 0
\(961\) 15.3185 0.494147
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 1.67447 + 2.90027i 0.0539031 + 0.0933629i
\(966\) 0 0
\(967\) 10.6439 18.4358i 0.342286 0.592856i −0.642571 0.766226i \(-0.722132\pi\)
0.984857 + 0.173370i \(0.0554656\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −22.1329 + 38.3352i −0.710277 + 1.23024i 0.254476 + 0.967079i \(0.418097\pi\)
−0.964753 + 0.263157i \(0.915236\pi\)
\(972\) 0 0
\(973\) −15.1821 26.2961i −0.486715 0.843016i
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −56.8291 −1.81812 −0.909062 0.416660i \(-0.863201\pi\)
−0.909062 + 0.416660i \(0.863201\pi\)
\(978\) 0 0
\(979\) −18.0826 + 10.4400i −0.577923 + 0.333664i
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 22.7404 39.3875i 0.725306 1.25627i −0.233542 0.972347i \(-0.575032\pi\)
0.958848 0.283920i \(-0.0916351\pi\)
\(984\) 0 0
\(985\) 1.38313 2.39566i 0.0440703 0.0763319i
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 74.6939i 2.37513i
\(990\) 0 0
\(991\) 8.64805 + 4.99295i 0.274714 + 0.158606i 0.631028 0.775760i \(-0.282633\pi\)
−0.356314 + 0.934366i \(0.615967\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 1.15224i 0.0365285i
\(996\) 0 0
\(997\) 11.2792 + 19.5361i 0.357215 + 0.618715i 0.987494 0.157654i \(-0.0503929\pi\)
−0.630279 + 0.776369i \(0.717060\pi\)
\(998\) 0 0
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (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 2736.2.dc.d.1889.4 16
3.2 odd 2 inner 2736.2.dc.d.1889.5 16
4.3 odd 2 684.2.bk.a.521.4 yes 16
12.11 even 2 684.2.bk.a.521.5 yes 16
19.12 odd 6 inner 2736.2.dc.d.449.5 16
57.50 even 6 inner 2736.2.dc.d.449.4 16
76.31 even 6 684.2.bk.a.449.5 yes 16
228.107 odd 6 684.2.bk.a.449.4 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
684.2.bk.a.449.4 16 228.107 odd 6
684.2.bk.a.449.5 yes 16 76.31 even 6
684.2.bk.a.521.4 yes 16 4.3 odd 2
684.2.bk.a.521.5 yes 16 12.11 even 2
2736.2.dc.d.449.4 16 57.50 even 6 inner
2736.2.dc.d.449.5 16 19.12 odd 6 inner
2736.2.dc.d.1889.4 16 1.1 even 1 trivial
2736.2.dc.d.1889.5 16 3.2 odd 2 inner