Properties

Label 2736.2.s.u.1873.1
Level $2736$
Weight $2$
Character 2736.1873
Analytic conductor $21.847$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [2736,2,Mod(577,2736)]
 
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, 0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2736.577");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2736.s (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: \(21.8470699930\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{7})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + 7x^{2} + 49 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 228)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 1873.1
Root \(-1.32288 + 2.29129i\) of defining polynomial
Character \(\chi\) \(=\) 2736.1873
Dual form 2736.2.s.u.577.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.822876 + 1.42526i) q^{5} +0.645751 q^{7} +O(q^{10})\) \(q+(-0.822876 + 1.42526i) q^{5} +0.645751 q^{7} +5.64575 q^{11} +(-3.14575 - 5.44860i) q^{13} +(3.64575 - 6.31463i) q^{17} +(-2.64575 + 3.46410i) q^{19} +(0.177124 + 0.306788i) q^{23} +(1.14575 + 1.98450i) q^{25} +(-1.64575 - 2.85052i) q^{29} -4.64575 q^{31} +(-0.531373 + 0.920365i) q^{35} -5.00000 q^{37} +(2.00000 - 3.46410i) q^{41} +(5.32288 - 9.21949i) q^{43} +(2.64575 + 4.58258i) q^{47} -6.58301 q^{49} +(-4.46863 - 7.73989i) q^{53} +(-4.64575 + 8.04668i) q^{55} +(-1.17712 + 2.03884i) q^{59} +(-2.50000 - 4.33013i) q^{61} +10.3542 q^{65} +(-0.968627 - 1.67771i) q^{67} +(5.00000 - 8.66025i) q^{71} +(-2.14575 + 3.71655i) q^{73} +3.64575 q^{77} +(4.32288 - 7.48744i) q^{79} +4.70850 q^{83} +(6.00000 + 10.3923i) q^{85} +(4.17712 + 7.23499i) q^{89} +(-2.03137 - 3.51844i) q^{91} +(-2.76013 - 6.62141i) q^{95} +(5.29150 - 9.16515i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{5} - 8 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 2 q^{5} - 8 q^{7} + 12 q^{11} - 2 q^{13} + 4 q^{17} + 6 q^{23} - 6 q^{25} + 4 q^{29} - 8 q^{31} - 18 q^{35} - 20 q^{37} + 8 q^{41} + 16 q^{43} + 16 q^{49} - 2 q^{53} - 8 q^{55} - 10 q^{59} - 10 q^{61} + 52 q^{65} + 12 q^{67} + 20 q^{71} + 2 q^{73} + 4 q^{77} + 12 q^{79} + 40 q^{83} + 24 q^{85} + 22 q^{89} - 24 q^{91} + 26 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(1009\) \(1217\) \(1711\) \(2053\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(1\) \(1\)

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
\(5\) −0.822876 + 1.42526i −0.368001 + 0.637397i −0.989253 0.146214i \(-0.953291\pi\)
0.621252 + 0.783611i \(0.286624\pi\)
\(6\) 0 0
\(7\) 0.645751 0.244071 0.122036 0.992526i \(-0.461058\pi\)
0.122036 + 0.992526i \(0.461058\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 5.64575 1.70226 0.851129 0.524957i \(-0.175918\pi\)
0.851129 + 0.524957i \(0.175918\pi\)
\(12\) 0 0
\(13\) −3.14575 5.44860i −0.872474 1.51117i −0.859429 0.511255i \(-0.829181\pi\)
−0.0130455 0.999915i \(-0.504153\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 3.64575 6.31463i 0.884225 1.53152i 0.0376247 0.999292i \(-0.488021\pi\)
0.846600 0.532230i \(-0.178646\pi\)
\(18\) 0 0
\(19\) −2.64575 + 3.46410i −0.606977 + 0.794719i
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 0.177124 + 0.306788i 0.0369330 + 0.0639698i 0.883901 0.467674i \(-0.154908\pi\)
−0.846968 + 0.531644i \(0.821575\pi\)
\(24\) 0 0
\(25\) 1.14575 + 1.98450i 0.229150 + 0.396900i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −1.64575 2.85052i −0.305608 0.529329i 0.671788 0.740743i \(-0.265526\pi\)
−0.977397 + 0.211414i \(0.932193\pi\)
\(30\) 0 0
\(31\) −4.64575 −0.834402 −0.417201 0.908814i \(-0.636989\pi\)
−0.417201 + 0.908814i \(0.636989\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −0.531373 + 0.920365i −0.0898184 + 0.155570i
\(36\) 0 0
\(37\) −5.00000 −0.821995 −0.410997 0.911636i \(-0.634819\pi\)
−0.410997 + 0.911636i \(0.634819\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 2.00000 3.46410i 0.312348 0.541002i −0.666523 0.745485i \(-0.732218\pi\)
0.978870 + 0.204483i \(0.0655513\pi\)
\(42\) 0 0
\(43\) 5.32288 9.21949i 0.811731 1.40596i −0.0999207 0.994995i \(-0.531859\pi\)
0.911652 0.410964i \(-0.134808\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 2.64575 + 4.58258i 0.385922 + 0.668437i 0.991897 0.127047i \(-0.0405499\pi\)
−0.605974 + 0.795484i \(0.707217\pi\)
\(48\) 0 0
\(49\) −6.58301 −0.940429
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −4.46863 7.73989i −0.613813 1.06316i −0.990591 0.136852i \(-0.956301\pi\)
0.376778 0.926303i \(-0.377032\pi\)
\(54\) 0 0
\(55\) −4.64575 + 8.04668i −0.626433 + 1.08501i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −1.17712 + 2.03884i −0.153249 + 0.265434i −0.932420 0.361377i \(-0.882307\pi\)
0.779171 + 0.626811i \(0.215640\pi\)
\(60\) 0 0
\(61\) −2.50000 4.33013i −0.320092 0.554416i 0.660415 0.750901i \(-0.270381\pi\)
−0.980507 + 0.196485i \(0.937047\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 10.3542 1.28429
\(66\) 0 0
\(67\) −0.968627 1.67771i −0.118337 0.204965i 0.800772 0.598969i \(-0.204423\pi\)
−0.919109 + 0.394004i \(0.871090\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 5.00000 8.66025i 0.593391 1.02778i −0.400381 0.916349i \(-0.631122\pi\)
0.993772 0.111434i \(-0.0355445\pi\)
\(72\) 0 0
\(73\) −2.14575 + 3.71655i −0.251141 + 0.434989i −0.963840 0.266481i \(-0.914139\pi\)
0.712699 + 0.701470i \(0.247473\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 3.64575 0.415472
\(78\) 0 0
\(79\) 4.32288 7.48744i 0.486362 0.842403i −0.513516 0.858080i \(-0.671657\pi\)
0.999877 + 0.0156774i \(0.00499048\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 4.70850 0.516825 0.258412 0.966035i \(-0.416801\pi\)
0.258412 + 0.966035i \(0.416801\pi\)
\(84\) 0 0
\(85\) 6.00000 + 10.3923i 0.650791 + 1.12720i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 4.17712 + 7.23499i 0.442774 + 0.766908i 0.997894 0.0648628i \(-0.0206610\pi\)
−0.555120 + 0.831770i \(0.687328\pi\)
\(90\) 0 0
\(91\) −2.03137 3.51844i −0.212946 0.368833i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −2.76013 6.62141i −0.283183 0.679343i
\(96\) 0 0
\(97\) 5.29150 9.16515i 0.537271 0.930580i −0.461779 0.886995i \(-0.652789\pi\)
0.999050 0.0435851i \(-0.0138780\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 5.93725 + 10.2836i 0.590779 + 1.02326i 0.994128 + 0.108213i \(0.0345128\pi\)
−0.403349 + 0.915046i \(0.632154\pi\)
\(102\) 0 0
\(103\) 7.93725 0.782081 0.391040 0.920373i \(-0.372115\pi\)
0.391040 + 0.920373i \(0.372115\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 14.0000 1.35343 0.676716 0.736245i \(-0.263403\pi\)
0.676716 + 0.736245i \(0.263403\pi\)
\(108\) 0 0
\(109\) 9.64575 16.7069i 0.923895 1.60023i 0.130567 0.991439i \(-0.458320\pi\)
0.793328 0.608794i \(-0.208347\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 0.354249 0.0333249 0.0166625 0.999861i \(-0.494696\pi\)
0.0166625 + 0.999861i \(0.494696\pi\)
\(114\) 0 0
\(115\) −0.583005 −0.0543655
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 2.35425 4.07768i 0.215814 0.373800i
\(120\) 0 0
\(121\) 20.8745 1.89768
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −12.0000 −1.07331
\(126\) 0 0
\(127\) 3.64575 + 6.31463i 0.323508 + 0.560332i 0.981209 0.192946i \(-0.0618044\pi\)
−0.657701 + 0.753279i \(0.728471\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −3.00000 + 5.19615i −0.262111 + 0.453990i −0.966803 0.255524i \(-0.917752\pi\)
0.704692 + 0.709514i \(0.251085\pi\)
\(132\) 0 0
\(133\) −1.70850 + 2.23695i −0.148146 + 0.193968i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 1.35425 + 2.34563i 0.115701 + 0.200400i 0.918060 0.396442i \(-0.129755\pi\)
−0.802359 + 0.596842i \(0.796422\pi\)
\(138\) 0 0
\(139\) 0.322876 + 0.559237i 0.0273860 + 0.0474339i 0.879394 0.476096i \(-0.157948\pi\)
−0.852008 + 0.523529i \(0.824615\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −17.7601 30.7614i −1.48518 2.57240i
\(144\) 0 0
\(145\) 5.41699 0.449857
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 1.82288 3.15731i 0.149336 0.258657i −0.781646 0.623722i \(-0.785620\pi\)
0.930982 + 0.365065i \(0.118953\pi\)
\(150\) 0 0
\(151\) 11.2915 0.918889 0.459445 0.888206i \(-0.348048\pi\)
0.459445 + 0.888206i \(0.348048\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 3.82288 6.62141i 0.307061 0.531845i
\(156\) 0 0
\(157\) 0.145751 0.252449i 0.0116322 0.0201476i −0.860151 0.510040i \(-0.829631\pi\)
0.871783 + 0.489892i \(0.162964\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0.114378 + 0.198109i 0.00901427 + 0.0156132i
\(162\) 0 0
\(163\) −15.9373 −1.24830 −0.624151 0.781304i \(-0.714555\pi\)
−0.624151 + 0.781304i \(0.714555\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −8.46863 14.6681i −0.655322 1.13505i −0.981813 0.189851i \(-0.939200\pi\)
0.326491 0.945200i \(-0.394134\pi\)
\(168\) 0 0
\(169\) −13.2915 + 23.0216i −1.02242 + 1.77089i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 10.9373 18.9439i 0.831544 1.44028i −0.0652695 0.997868i \(-0.520791\pi\)
0.896813 0.442409i \(-0.145876\pi\)
\(174\) 0 0
\(175\) 0.739870 + 1.28149i 0.0559289 + 0.0968718i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −15.6458 −1.16942 −0.584709 0.811243i \(-0.698791\pi\)
−0.584709 + 0.811243i \(0.698791\pi\)
\(180\) 0 0
\(181\) 2.70850 + 4.69126i 0.201321 + 0.348698i 0.948954 0.315414i \(-0.102143\pi\)
−0.747633 + 0.664112i \(0.768810\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 4.11438 7.12631i 0.302495 0.523937i
\(186\) 0 0
\(187\) 20.5830 35.6508i 1.50518 2.60705i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 14.9373 1.08082 0.540411 0.841401i \(-0.318269\pi\)
0.540411 + 0.841401i \(0.318269\pi\)
\(192\) 0 0
\(193\) 10.0830 17.4643i 0.725791 1.25711i −0.232857 0.972511i \(-0.574807\pi\)
0.958648 0.284595i \(-0.0918592\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 12.3542 0.880204 0.440102 0.897948i \(-0.354942\pi\)
0.440102 + 0.897948i \(0.354942\pi\)
\(198\) 0 0
\(199\) 1.96863 + 3.40976i 0.139552 + 0.241712i 0.927327 0.374252i \(-0.122100\pi\)
−0.787775 + 0.615963i \(0.788767\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −1.06275 1.84073i −0.0745902 0.129194i
\(204\) 0 0
\(205\) 3.29150 + 5.70105i 0.229889 + 0.398179i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −14.9373 + 19.5575i −1.03323 + 1.35282i
\(210\) 0 0
\(211\) 2.67712 4.63692i 0.184301 0.319218i −0.759040 0.651044i \(-0.774331\pi\)
0.943341 + 0.331826i \(0.107665\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 8.76013 + 15.1730i 0.597436 + 1.03479i
\(216\) 0 0
\(217\) −3.00000 −0.203653
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −45.8745 −3.08585
\(222\) 0 0
\(223\) −5.32288 + 9.21949i −0.356446 + 0.617383i −0.987364 0.158467i \(-0.949345\pi\)
0.630918 + 0.775849i \(0.282678\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −21.5203 −1.42835 −0.714175 0.699967i \(-0.753198\pi\)
−0.714175 + 0.699967i \(0.753198\pi\)
\(228\) 0 0
\(229\) −20.2915 −1.34090 −0.670450 0.741955i \(-0.733899\pi\)
−0.670450 + 0.741955i \(0.733899\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 13.9373 24.1400i 0.913060 1.58147i 0.103343 0.994646i \(-0.467046\pi\)
0.809717 0.586820i \(-0.199620\pi\)
\(234\) 0 0
\(235\) −8.70850 −0.568080
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −10.9373 −0.707472 −0.353736 0.935345i \(-0.615089\pi\)
−0.353736 + 0.935345i \(0.615089\pi\)
\(240\) 0 0
\(241\) 10.4373 + 18.0779i 0.672323 + 1.16450i 0.977244 + 0.212119i \(0.0680366\pi\)
−0.304921 + 0.952378i \(0.598630\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 5.41699 9.38251i 0.346079 0.599427i
\(246\) 0 0
\(247\) 27.1974 + 3.51844i 1.73053 + 0.223873i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 1.35425 + 2.34563i 0.0854794 + 0.148055i 0.905595 0.424143i \(-0.139424\pi\)
−0.820116 + 0.572197i \(0.806091\pi\)
\(252\) 0 0
\(253\) 1.00000 + 1.73205i 0.0628695 + 0.108893i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 5.17712 + 8.96704i 0.322940 + 0.559349i 0.981093 0.193535i \(-0.0619954\pi\)
−0.658153 + 0.752884i \(0.728662\pi\)
\(258\) 0 0
\(259\) −3.22876 −0.200625
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −9.00000 + 15.5885i −0.554964 + 0.961225i 0.442943 + 0.896550i \(0.353935\pi\)
−0.997906 + 0.0646755i \(0.979399\pi\)
\(264\) 0 0
\(265\) 14.7085 0.903536
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −4.17712 + 7.23499i −0.254684 + 0.441125i −0.964810 0.262950i \(-0.915305\pi\)
0.710126 + 0.704075i \(0.248638\pi\)
\(270\) 0 0
\(271\) −5.29150 + 9.16515i −0.321436 + 0.556743i −0.980785 0.195094i \(-0.937499\pi\)
0.659349 + 0.751837i \(0.270832\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 6.46863 + 11.2040i 0.390073 + 0.675626i
\(276\) 0 0
\(277\) −8.00000 −0.480673 −0.240337 0.970690i \(-0.577258\pi\)
−0.240337 + 0.970690i \(0.577258\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 4.46863 + 7.73989i 0.266576 + 0.461723i 0.967975 0.251045i \(-0.0807744\pi\)
−0.701399 + 0.712768i \(0.747441\pi\)
\(282\) 0 0
\(283\) −13.2915 + 23.0216i −0.790098 + 1.36849i 0.135808 + 0.990735i \(0.456637\pi\)
−0.925906 + 0.377754i \(0.876696\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 1.29150 2.23695i 0.0762350 0.132043i
\(288\) 0 0
\(289\) −18.0830 31.3207i −1.06371 1.84239i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 3.41699 0.199623 0.0998115 0.995006i \(-0.468176\pi\)
0.0998115 + 0.995006i \(0.468176\pi\)
\(294\) 0 0
\(295\) −1.93725 3.35542i −0.112791 0.195360i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 1.11438 1.93016i 0.0644462 0.111624i
\(300\) 0 0
\(301\) 3.43725 5.95350i 0.198120 0.343154i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 8.22876 0.471177
\(306\) 0 0
\(307\) 1.93725 3.35542i 0.110565 0.191504i −0.805433 0.592686i \(-0.798067\pi\)
0.915998 + 0.401182i \(0.131401\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 32.9373 1.86770 0.933850 0.357664i \(-0.116427\pi\)
0.933850 + 0.357664i \(0.116427\pi\)
\(312\) 0 0
\(313\) 4.35425 + 7.54178i 0.246117 + 0.426287i 0.962445 0.271477i \(-0.0875120\pi\)
−0.716328 + 0.697763i \(0.754179\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 2.46863 + 4.27579i 0.138652 + 0.240152i 0.926987 0.375095i \(-0.122390\pi\)
−0.788335 + 0.615247i \(0.789056\pi\)
\(318\) 0 0
\(319\) −9.29150 16.0934i −0.520224 0.901055i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 12.2288 + 29.3362i 0.680426 + 1.63231i
\(324\) 0 0
\(325\) 7.20850 12.4855i 0.399855 0.692570i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 1.70850 + 2.95920i 0.0941925 + 0.163146i
\(330\) 0 0
\(331\) −5.22876 −0.287398 −0.143699 0.989621i \(-0.545900\pi\)
−0.143699 + 0.989621i \(0.545900\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 3.18824 0.174192
\(336\) 0 0
\(337\) 4.85425 8.40781i 0.264428 0.458002i −0.702986 0.711204i \(-0.748150\pi\)
0.967414 + 0.253202i \(0.0814836\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −26.2288 −1.42037
\(342\) 0 0
\(343\) −8.77124 −0.473603
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 14.4059 24.9517i 0.773348 1.33948i −0.162370 0.986730i \(-0.551914\pi\)
0.935718 0.352748i \(-0.114753\pi\)
\(348\) 0 0
\(349\) −20.8745 −1.11739 −0.558693 0.829374i \(-0.688697\pi\)
−0.558693 + 0.829374i \(0.688697\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −4.93725 −0.262784 −0.131392 0.991331i \(-0.541945\pi\)
−0.131392 + 0.991331i \(0.541945\pi\)
\(354\) 0 0
\(355\) 8.22876 + 14.2526i 0.436737 + 0.756451i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −12.0000 + 20.7846i −0.633336 + 1.09697i 0.353529 + 0.935423i \(0.384981\pi\)
−0.986865 + 0.161546i \(0.948352\pi\)
\(360\) 0 0
\(361\) −5.00000 18.3303i −0.263158 0.964753i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −3.53137 6.11652i −0.184841 0.320153i
\(366\) 0 0
\(367\) 6.61438 + 11.4564i 0.345268 + 0.598021i 0.985402 0.170241i \(-0.0544548\pi\)
−0.640135 + 0.768263i \(0.721121\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −2.88562 4.99804i −0.149814 0.259485i
\(372\) 0 0
\(373\) −4.00000 −0.207112 −0.103556 0.994624i \(-0.533022\pi\)
−0.103556 + 0.994624i \(0.533022\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −10.3542 + 17.9341i −0.533271 + 0.923652i
\(378\) 0 0
\(379\) −28.5203 −1.46499 −0.732494 0.680774i \(-0.761644\pi\)
−0.732494 + 0.680774i \(0.761644\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −3.17712 + 5.50294i −0.162343 + 0.281187i −0.935709 0.352774i \(-0.885239\pi\)
0.773365 + 0.633961i \(0.218572\pi\)
\(384\) 0 0
\(385\) −3.00000 + 5.19615i −0.152894 + 0.264820i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −18.1144 31.3750i −0.918435 1.59078i −0.801792 0.597603i \(-0.796120\pi\)
−0.116643 0.993174i \(-0.537213\pi\)
\(390\) 0 0
\(391\) 2.58301 0.130628
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 7.11438 + 12.3225i 0.357963 + 0.620010i
\(396\) 0 0
\(397\) 5.85425 10.1399i 0.293816 0.508905i −0.680893 0.732383i \(-0.738408\pi\)
0.974709 + 0.223479i \(0.0717413\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 9.82288 17.0137i 0.490531 0.849625i −0.509410 0.860524i \(-0.670136\pi\)
0.999941 + 0.0108996i \(0.00346951\pi\)
\(402\) 0 0
\(403\) 14.6144 + 25.3128i 0.727994 + 1.26092i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −28.2288 −1.39925
\(408\) 0 0
\(409\) 7.64575 + 13.2428i 0.378058 + 0.654816i 0.990780 0.135483i \(-0.0432586\pi\)
−0.612722 + 0.790299i \(0.709925\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −0.760130 + 1.31658i −0.0374035 + 0.0647848i
\(414\) 0 0
\(415\) −3.87451 + 6.71084i −0.190192 + 0.329422i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 7.06275 0.345038 0.172519 0.985006i \(-0.444809\pi\)
0.172519 + 0.985006i \(0.444809\pi\)
\(420\) 0 0
\(421\) −16.2288 + 28.1090i −0.790941 + 1.36995i 0.134444 + 0.990921i \(0.457075\pi\)
−0.925385 + 0.379029i \(0.876258\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 16.7085 0.810481
\(426\) 0 0
\(427\) −1.61438 2.79619i −0.0781252 0.135317i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −9.22876 15.9847i −0.444534 0.769955i 0.553486 0.832858i \(-0.313297\pi\)
−0.998020 + 0.0629037i \(0.979964\pi\)
\(432\) 0 0
\(433\) −0.145751 0.252449i −0.00700436 0.0121319i 0.862502 0.506054i \(-0.168896\pi\)
−0.869506 + 0.493922i \(0.835563\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −1.53137 0.198109i −0.0732555 0.00947684i
\(438\) 0 0
\(439\) 9.26013 16.0390i 0.441962 0.765500i −0.555873 0.831267i \(-0.687616\pi\)
0.997835 + 0.0657667i \(0.0209493\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −4.35425 7.54178i −0.206877 0.358321i 0.743852 0.668344i \(-0.232997\pi\)
−0.950729 + 0.310023i \(0.899663\pi\)
\(444\) 0 0
\(445\) −13.7490 −0.651766
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 3.29150 0.155336 0.0776678 0.996979i \(-0.475253\pi\)
0.0776678 + 0.996979i \(0.475253\pi\)
\(450\) 0 0
\(451\) 11.2915 19.5575i 0.531696 0.920925i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 6.68627 0.313457
\(456\) 0 0
\(457\) −3.12549 −0.146204 −0.0731022 0.997324i \(-0.523290\pi\)
−0.0731022 + 0.997324i \(0.523290\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −20.7601 + 35.9576i −0.966896 + 1.67471i −0.262462 + 0.964942i \(0.584535\pi\)
−0.704433 + 0.709770i \(0.748799\pi\)
\(462\) 0 0
\(463\) −6.77124 −0.314686 −0.157343 0.987544i \(-0.550293\pi\)
−0.157343 + 0.987544i \(0.550293\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 33.1660 1.53474 0.767370 0.641205i \(-0.221565\pi\)
0.767370 + 0.641205i \(0.221565\pi\)
\(468\) 0 0
\(469\) −0.625492 1.08338i −0.0288825 0.0500260i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 30.0516 52.0510i 1.38178 2.39331i
\(474\) 0 0
\(475\) −9.90588 1.28149i −0.454513 0.0587989i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 21.5830 + 37.3829i 0.986153 + 1.70807i 0.636698 + 0.771113i \(0.280300\pi\)
0.349455 + 0.936953i \(0.386367\pi\)
\(480\) 0 0
\(481\) 15.7288 + 27.2430i 0.717170 + 1.24217i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 8.70850 + 15.0836i 0.395432 + 0.684909i
\(486\) 0 0
\(487\) −11.2915 −0.511667 −0.255833 0.966721i \(-0.582350\pi\)
−0.255833 + 0.966721i \(0.582350\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −9.58301 + 16.5983i −0.432475 + 0.749069i −0.997086 0.0762887i \(-0.975693\pi\)
0.564611 + 0.825357i \(0.309026\pi\)
\(492\) 0 0
\(493\) −24.0000 −1.08091
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 3.22876 5.59237i 0.144830 0.250852i
\(498\) 0 0
\(499\) 17.5516 30.4003i 0.785719 1.36091i −0.142850 0.989744i \(-0.545627\pi\)
0.928569 0.371161i \(-0.121040\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −15.6458 27.0992i −0.697610 1.20830i −0.969293 0.245909i \(-0.920914\pi\)
0.271683 0.962387i \(-0.412420\pi\)
\(504\) 0 0
\(505\) −19.5425 −0.869629
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 20.1660 + 34.9286i 0.893843 + 1.54818i 0.835230 + 0.549900i \(0.185334\pi\)
0.0586123 + 0.998281i \(0.481332\pi\)
\(510\) 0 0
\(511\) −1.38562 + 2.39997i −0.0612963 + 0.106168i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −6.53137 + 11.3127i −0.287807 + 0.498496i
\(516\) 0 0
\(517\) 14.9373 + 25.8721i 0.656940 + 1.13785i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 12.3542 0.541249 0.270625 0.962685i \(-0.412770\pi\)
0.270625 + 0.962685i \(0.412770\pi\)
\(522\) 0 0
\(523\) 17.1974 + 29.7867i 0.751989 + 1.30248i 0.946857 + 0.321654i \(0.104239\pi\)
−0.194868 + 0.980829i \(0.562428\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −16.9373 + 29.3362i −0.737798 + 1.27790i
\(528\) 0 0
\(529\) 11.4373 19.8099i 0.497272 0.861300i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −25.1660 −1.09006
\(534\) 0 0
\(535\) −11.5203 + 19.9537i −0.498064 + 0.862673i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −37.1660 −1.60085
\(540\) 0 0
\(541\) 2.43725 + 4.22145i 0.104786 + 0.181494i 0.913651 0.406500i \(-0.133251\pi\)
−0.808865 + 0.587995i \(0.799918\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 15.8745 + 27.4955i 0.679989 + 1.17778i
\(546\) 0 0
\(547\) 12.6144 + 21.8487i 0.539352 + 0.934185i 0.998939 + 0.0460522i \(0.0146640\pi\)
−0.459587 + 0.888133i \(0.652003\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 14.2288 + 1.84073i 0.606165 + 0.0784177i
\(552\) 0 0
\(553\) 2.79150 4.83502i 0.118707 0.205606i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −2.06275 3.57278i −0.0874014 0.151384i 0.819011 0.573778i \(-0.194523\pi\)
−0.906412 + 0.422395i \(0.861190\pi\)
\(558\) 0 0
\(559\) −66.9778 −2.83286
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 6.00000 0.252870 0.126435 0.991975i \(-0.459647\pi\)
0.126435 + 0.991975i \(0.459647\pi\)
\(564\) 0 0
\(565\) −0.291503 + 0.504897i −0.0122636 + 0.0212412i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 1.16601 0.0488817 0.0244409 0.999701i \(-0.492219\pi\)
0.0244409 + 0.999701i \(0.492219\pi\)
\(570\) 0 0
\(571\) 11.9373 0.499559 0.249779 0.968303i \(-0.419642\pi\)
0.249779 + 0.968303i \(0.419642\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −0.405881 + 0.703006i −0.0169264 + 0.0293174i
\(576\) 0 0
\(577\) −11.2915 −0.470071 −0.235036 0.971987i \(-0.575521\pi\)
−0.235036 + 0.971987i \(0.575521\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 3.04052 0.126142
\(582\) 0 0
\(583\) −25.2288 43.6975i −1.04487 1.80977i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −0.114378 + 0.198109i −0.00472090 + 0.00817683i −0.868376 0.495906i \(-0.834836\pi\)
0.863655 + 0.504083i \(0.168169\pi\)
\(588\) 0 0
\(589\) 12.2915 16.0934i 0.506463 0.663115i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −3.46863 6.00784i −0.142439 0.246712i 0.785975 0.618258i \(-0.212161\pi\)
−0.928415 + 0.371546i \(0.878828\pi\)
\(594\) 0 0
\(595\) 3.87451 + 6.71084i 0.158839 + 0.275118i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 1.17712 + 2.03884i 0.0480960 + 0.0833047i 0.889071 0.457769i \(-0.151351\pi\)
−0.840975 + 0.541074i \(0.818018\pi\)
\(600\) 0 0
\(601\) −30.2915 −1.23562 −0.617808 0.786329i \(-0.711979\pi\)
−0.617808 + 0.786329i \(0.711979\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −17.1771 + 29.7517i −0.698349 + 1.20958i
\(606\) 0 0
\(607\) 20.0627 0.814322 0.407161 0.913356i \(-0.366519\pi\)
0.407161 + 0.913356i \(0.366519\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 16.6458 28.8313i 0.673415 1.16639i
\(612\) 0 0
\(613\) −16.5830 + 28.7226i −0.669781 + 1.16010i 0.308184 + 0.951327i \(0.400279\pi\)
−0.977965 + 0.208768i \(0.933055\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 17.4686 + 30.2565i 0.703260 + 1.21808i 0.967316 + 0.253575i \(0.0816065\pi\)
−0.264055 + 0.964508i \(0.585060\pi\)
\(618\) 0 0
\(619\) −8.06275 −0.324069 −0.162035 0.986785i \(-0.551806\pi\)
−0.162035 + 0.986785i \(0.551806\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 2.69738 + 4.67201i 0.108068 + 0.187180i
\(624\) 0 0
\(625\) 4.14575 7.18065i 0.165830 0.287226i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −18.2288 + 31.5731i −0.726828 + 1.25890i
\(630\) 0 0
\(631\) −1.03137 1.78639i −0.0410583 0.0711151i 0.844766 0.535136i \(-0.179740\pi\)
−0.885824 + 0.464021i \(0.846406\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −12.0000 −0.476205
\(636\) 0 0
\(637\) 20.7085 + 35.8682i 0.820501 + 1.42115i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −10.2915 + 17.8254i −0.406490 + 0.704061i −0.994494 0.104797i \(-0.966581\pi\)
0.588004 + 0.808858i \(0.299914\pi\)
\(642\) 0 0
\(643\) −15.0314 + 26.0351i −0.592779 + 1.02672i 0.401077 + 0.916045i \(0.368636\pi\)
−0.993856 + 0.110680i \(0.964697\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 27.2915 1.07294 0.536470 0.843919i \(-0.319758\pi\)
0.536470 + 0.843919i \(0.319758\pi\)
\(648\) 0 0
\(649\) −6.64575 + 11.5108i −0.260869 + 0.451838i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 8.12549 0.317975 0.158988 0.987281i \(-0.449177\pi\)
0.158988 + 0.987281i \(0.449177\pi\)
\(654\) 0 0
\(655\) −4.93725 8.55157i −0.192914 0.334138i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −3.88562 6.73009i −0.151362 0.262167i 0.780366 0.625323i \(-0.215033\pi\)
−0.931729 + 0.363156i \(0.881699\pi\)
\(660\) 0 0
\(661\) 1.00000 + 1.73205i 0.0388955 + 0.0673690i 0.884818 0.465937i \(-0.154283\pi\)
−0.845922 + 0.533306i \(0.820949\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −1.78236 4.27579i −0.0691169 0.165808i
\(666\) 0 0
\(667\) 0.583005 1.00979i 0.0225741 0.0390994i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −14.1144 24.4468i −0.544880 0.943759i
\(672\) 0 0
\(673\) 38.8745 1.49850 0.749251 0.662286i \(-0.230414\pi\)
0.749251 + 0.662286i \(0.230414\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 19.1660 0.736610 0.368305 0.929705i \(-0.379938\pi\)
0.368305 + 0.929705i \(0.379938\pi\)
\(678\) 0 0
\(679\) 3.41699 5.91841i 0.131132 0.227128i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −26.2288 −1.00362 −0.501808 0.864979i \(-0.667332\pi\)
−0.501808 + 0.864979i \(0.667332\pi\)
\(684\) 0 0
\(685\) −4.45751 −0.170313
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −28.1144 + 48.6955i −1.07107 + 1.85515i
\(690\) 0 0
\(691\) −29.1660 −1.10953 −0.554764 0.832008i \(-0.687191\pi\)
−0.554764 + 0.832008i \(0.687191\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −1.06275 −0.0403123
\(696\) 0 0
\(697\) −14.5830 25.2585i −0.552371 0.956734i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −7.05163 + 12.2138i −0.266336 + 0.461308i −0.967913 0.251286i \(-0.919147\pi\)
0.701576 + 0.712594i \(0.252480\pi\)
\(702\) 0 0
\(703\) 13.2288 17.3205i 0.498932 0.653255i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 3.83399 + 6.64066i 0.144192 + 0.249748i
\(708\) 0 0
\(709\) −8.79150 15.2273i −0.330172 0.571874i 0.652374 0.757898i \(-0.273773\pi\)
−0.982545 + 0.186023i \(0.940440\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −0.822876 1.42526i −0.0308169 0.0533765i
\(714\) 0 0
\(715\) 58.4575 2.18619
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −7.46863 + 12.9360i −0.278533 + 0.482433i −0.971020 0.238997i \(-0.923181\pi\)
0.692488 + 0.721430i \(0.256515\pi\)
\(720\) 0 0
\(721\) 5.12549 0.190883
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 3.77124 6.53199i 0.140060 0.242592i
\(726\) 0 0
\(727\) −6.26013 + 10.8429i −0.232175 + 0.402140i −0.958448 0.285267i \(-0.907918\pi\)
0.726273 + 0.687407i \(0.241251\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −38.8118 67.2239i −1.43550 2.48637i
\(732\) 0 0
\(733\) 29.1660 1.07727 0.538636 0.842539i \(-0.318940\pi\)
0.538636 + 0.842539i \(0.318940\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −5.46863 9.47194i −0.201439 0.348903i
\(738\) 0 0
\(739\) −13.6771 + 23.6895i −0.503121 + 0.871431i 0.496872 + 0.867824i \(0.334482\pi\)
−0.999993 + 0.00360775i \(0.998852\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −10.1144 + 17.5186i −0.371061 + 0.642696i −0.989729 0.142956i \(-0.954339\pi\)
0.618668 + 0.785652i \(0.287672\pi\)
\(744\) 0 0
\(745\) 3.00000 + 5.19615i 0.109911 + 0.190372i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 9.04052 0.330333
\(750\) 0 0
\(751\) 1.32288 + 2.29129i 0.0482724 + 0.0836103i 0.889152 0.457612i \(-0.151295\pi\)
−0.840880 + 0.541222i \(0.817962\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −9.29150 + 16.0934i −0.338152 + 0.585697i
\(756\) 0 0
\(757\) 3.79150 6.56708i 0.137805 0.238684i −0.788861 0.614572i \(-0.789329\pi\)
0.926665 + 0.375888i \(0.122662\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −1.52026 −0.0551094 −0.0275547 0.999620i \(-0.508772\pi\)
−0.0275547 + 0.999620i \(0.508772\pi\)
\(762\) 0 0
\(763\) 6.22876 10.7885i 0.225496 0.390571i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 14.8118 0.534822
\(768\) 0 0
\(769\) −4.79150 8.29913i −0.172786 0.299274i 0.766607 0.642117i \(-0.221944\pi\)
−0.939393 + 0.342843i \(0.888610\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −12.8745 22.2993i −0.463064 0.802050i 0.536048 0.844188i \(-0.319917\pi\)
−0.999112 + 0.0421374i \(0.986583\pi\)
\(774\) 0 0
\(775\) −5.32288 9.21949i −0.191203 0.331174i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 6.70850 + 16.0934i 0.240357 + 0.576604i
\(780\) 0 0
\(781\) 28.2288 48.8936i 1.01010 1.74955i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 0.239870 + 0.415468i 0.00856134 + 0.0148287i
\(786\) 0 0
\(787\) −27.8118 −0.991382 −0.495691 0.868499i \(-0.665085\pi\)
−0.495691 + 0.868499i \(0.665085\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0.228757 0.00813365
\(792\) 0 0
\(793\) −15.7288 + 27.2430i −0.558545 + 0.967427i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −34.7085 −1.22944 −0.614719 0.788746i \(-0.710731\pi\)
−0.614719 + 0.788746i \(0.710731\pi\)
\(798\) 0 0
\(799\) 38.5830 1.36497
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −12.1144 + 20.9827i −0.427507 + 0.740464i
\(804\) 0 0
\(805\) −0.376476 −0.0132690
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −4.93725 −0.173585 −0.0867923 0.996226i \(-0.527662\pi\)
−0.0867923 + 0.996226i \(0.527662\pi\)
\(810\) 0 0
\(811\) −24.2288 41.9654i −0.850787 1.47361i −0.880499 0.474047i \(-0.842793\pi\)
0.0297126 0.999558i \(-0.490541\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 13.1144 22.7148i 0.459377 0.795664i
\(816\) 0 0
\(817\) 17.8542 + 42.8315i 0.624641 + 1.49848i
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −22.9373 39.7285i −0.800516 1.38653i −0.919277 0.393611i \(-0.871226\pi\)
0.118761 0.992923i \(-0.462108\pi\)
\(822\) 0 0
\(823\) 12.3542 + 21.3982i 0.430642 + 0.745894i 0.996929 0.0783145i \(-0.0249538\pi\)
−0.566287 + 0.824208i \(0.691620\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −13.6458 23.6351i −0.474509 0.821874i 0.525065 0.851062i \(-0.324041\pi\)
−0.999574 + 0.0291882i \(0.990708\pi\)
\(828\) 0 0
\(829\) −30.4170 −1.05643 −0.528213 0.849112i \(-0.677138\pi\)
−0.528213 + 0.849112i \(0.677138\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −24.0000 + 41.5692i −0.831551 + 1.44029i
\(834\) 0 0
\(835\) 27.8745 0.964637
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −2.17712 + 3.77089i −0.0751627 + 0.130186i −0.901157 0.433493i \(-0.857281\pi\)
0.825994 + 0.563678i \(0.190614\pi\)
\(840\) 0 0
\(841\) 9.08301 15.7322i 0.313207 0.542491i
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −21.8745 37.8878i −0.752506 1.30338i
\(846\) 0 0
\(847\) 13.4797 0.463169
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −0.885622 1.53394i −0.0303587 0.0525828i
\(852\) 0 0
\(853\) 14.3745 24.8974i 0.492174 0.852470i −0.507786 0.861483i \(-0.669536\pi\)
0.999959 + 0.00901349i \(0.00286912\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 21.0000 36.3731i 0.717346 1.24248i −0.244701 0.969599i \(-0.578690\pi\)
0.962048 0.272882i \(-0.0879768\pi\)
\(858\) 0 0
\(859\) −10.9686 18.9982i −0.374245 0.648211i 0.615969 0.787770i \(-0.288765\pi\)
−0.990214 + 0.139560i \(0.955431\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −37.2915 −1.26942 −0.634709 0.772751i \(-0.718880\pi\)
−0.634709 + 0.772751i \(0.718880\pi\)
\(864\) 0 0
\(865\) 18.0000 + 31.1769i 0.612018 + 1.06005i
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 24.4059 42.2722i 0.827913 1.43399i
\(870\) 0 0
\(871\) −6.09412 + 10.5553i −0.206491 + 0.357654i
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −7.74902 −0.261965
\(876\) 0 0
\(877\) −12.0830 + 20.9284i −0.408014 + 0.706701i −0.994667 0.103137i \(-0.967112\pi\)
0.586653 + 0.809838i \(0.300445\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 48.6863 1.64028 0.820141 0.572161i \(-0.193895\pi\)
0.820141 + 0.572161i \(0.193895\pi\)
\(882\) 0 0
\(883\) 11.3229 + 19.6118i 0.381045 + 0.659989i 0.991212 0.132283i \(-0.0422309\pi\)
−0.610167 + 0.792273i \(0.708898\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 21.0516 + 36.4625i 0.706845 + 1.22429i 0.966022 + 0.258461i \(0.0832153\pi\)
−0.259177 + 0.965830i \(0.583451\pi\)
\(888\) 0 0
\(889\) 2.35425 + 4.07768i 0.0789590 + 0.136761i
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −22.8745 2.95920i −0.765466 0.0990260i
\(894\) 0 0
\(895\) 12.8745 22.2993i 0.430347 0.745383i
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 7.64575 + 13.2428i 0.255000 + 0.441673i
\(900\) 0 0
\(901\) −65.1660 −2.17099
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −8.91503 −0.296345
\(906\) 0 0
\(907\) −22.5830 + 39.1149i −0.749856 + 1.29879i 0.198035 + 0.980195i \(0.436544\pi\)
−0.947891 + 0.318594i \(0.896789\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −19.7490 −0.654314 −0.327157 0.944970i \(-0.606091\pi\)
−0.327157 + 0.944970i \(0.606091\pi\)
\(912\) 0 0
\(913\) 26.5830 0.879769
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −1.93725 + 3.35542i −0.0639738 + 0.110806i
\(918\) 0 0
\(919\) 25.2288 0.832220 0.416110 0.909314i \(-0.363393\pi\)
0.416110 + 0.909314i \(0.363393\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −62.9150 −2.07087
\(924\) 0 0
\(925\) −5.72876 9.92250i −0.188360 0.326250i
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 0.239870 0.415468i 0.00786989 0.0136311i −0.862064 0.506800i \(-0.830828\pi\)
0.869934 + 0.493169i \(0.164162\pi\)
\(930\) 0 0
\(931\) 17.4170 22.8042i 0.570819 0.747377i
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 33.8745 + 58.6724i 1.10781 + 1.91879i
\(936\) 0 0
\(937\) 3.50000 + 6.06218i 0.114340 + 0.198043i 0.917516 0.397699i \(-0.130191\pi\)
−0.803176 + 0.595742i \(0.796858\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 11.8745 + 20.5673i 0.387098 + 0.670473i 0.992058 0.125783i \(-0.0401442\pi\)
−0.604960 + 0.796256i \(0.706811\pi\)
\(942\) 0 0
\(943\) 1.41699 0.0461437
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 14.1660 24.5362i 0.460333 0.797321i −0.538644 0.842534i \(-0.681063\pi\)
0.998977 + 0.0452125i \(0.0143965\pi\)
\(948\) 0 0
\(949\) 27.0000 0.876457
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 3.23987 5.61162i 0.104950 0.181778i −0.808768 0.588128i \(-0.799865\pi\)
0.913718 + 0.406350i \(0.133199\pi\)
\(954\) 0 0
\(955\) −12.2915 + 21.2895i −0.397744 + 0.688912i
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0.874508 + 1.51469i 0.0282393 + 0.0489120i
\(960\) 0 0
\(961\) −9.41699 −0.303774
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 16.5941 + 28.7419i 0.534184 + 0.925233i
\(966\) 0 0
\(967\) 0.968627 1.67771i 0.0311489 0.0539516i −0.850031 0.526733i \(-0.823417\pi\)
0.881180 + 0.472782i \(0.156750\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −14.5203 + 25.1498i −0.465977 + 0.807096i −0.999245 0.0388502i \(-0.987630\pi\)
0.533268 + 0.845947i \(0.320964\pi\)
\(972\) 0 0
\(973\) 0.208497 + 0.361128i 0.00668412 + 0.0115772i
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −50.9150 −1.62892 −0.814458 0.580223i \(-0.802966\pi\)
−0.814458 + 0.580223i \(0.802966\pi\)
\(978\) 0 0
\(979\) 23.5830 + 40.8470i 0.753716 + 1.30547i
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −21.5314 + 37.2934i −0.686744 + 1.18948i 0.286141 + 0.958187i \(0.407627\pi\)
−0.972885 + 0.231288i \(0.925706\pi\)
\(984\) 0 0
\(985\) −10.1660 + 17.6080i −0.323916 + 0.561039i
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 3.77124 0.119919
\(990\) 0 0
\(991\) −1.96863 + 3.40976i −0.0625355 + 0.108315i −0.895598 0.444864i \(-0.853252\pi\)
0.833063 + 0.553179i \(0.186585\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −6.47974 −0.205422
\(996\) 0 0
\(997\) −23.0203 39.8723i −0.729059 1.26277i −0.957281 0.289158i \(-0.906625\pi\)
0.228222 0.973609i \(-0.426709\pi\)
\(998\) 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.s.u.1873.1 4
3.2 odd 2 912.2.q.g.49.2 4
4.3 odd 2 684.2.k.g.505.1 4
12.11 even 2 228.2.i.b.49.2 4
19.7 even 3 inner 2736.2.s.u.577.1 4
57.26 odd 6 912.2.q.g.577.2 4
76.7 odd 6 684.2.k.g.577.1 4
228.11 even 6 4332.2.a.h.1.1 2
228.83 even 6 228.2.i.b.121.2 yes 4
228.179 odd 6 4332.2.a.m.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
228.2.i.b.49.2 4 12.11 even 2
228.2.i.b.121.2 yes 4 228.83 even 6
684.2.k.g.505.1 4 4.3 odd 2
684.2.k.g.577.1 4 76.7 odd 6
912.2.q.g.49.2 4 3.2 odd 2
912.2.q.g.577.2 4 57.26 odd 6
2736.2.s.u.577.1 4 19.7 even 3 inner
2736.2.s.u.1873.1 4 1.1 even 1 trivial
4332.2.a.h.1.1 2 228.11 even 6
4332.2.a.m.1.1 2 228.179 odd 6