Properties

Label 2736.2.s.bc.1873.4
Level $2736$
Weight $2$
Character 2736.1873
Analytic conductor $21.847$
Analytic rank $0$
Dimension $8$
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: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 2x^{7} + 8x^{6} + 21x^{4} - 4x^{3} + 28x^{2} + 12x + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 1368)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 1873.4
Root \(0.643668 + 1.11487i\) of defining polynomial
Character \(\chi\) \(=\) 2736.1873
Dual form 2736.2.s.bc.577.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.95872 - 3.39260i) q^{5} -2.04306 q^{7} +O(q^{10})\) \(q+(1.95872 - 3.39260i) q^{5} -2.04306 q^{7} +1.91744 q^{11} +(2.13010 + 3.68945i) q^{13} +(3.04306 - 5.27073i) q^{17} +(-4.33039 - 0.497680i) q^{19} +(-3.42711 - 5.93592i) q^{23} +(-5.17316 - 8.96018i) q^{25} +(1.34277 + 2.32574i) q^{29} +1.46839 q^{31} +(-4.00178 + 6.93128i) q^{35} +3.93677 q^{37} +(1.70029 - 2.94499i) q^{41} +(3.77725 - 6.54239i) q^{43} +(4.96050 + 8.59183i) q^{47} -2.82591 q^{49} +(-4.91922 - 8.52033i) q^{53} +(3.75572 - 6.50510i) q^{55} +(-1.61595 + 2.79891i) q^{59} +(-4.70477 - 8.14891i) q^{61} +16.6891 q^{65} +(5.28173 + 9.14823i) q^{67} +(2.21715 - 3.84021i) q^{71} +(-6.33488 + 10.9723i) q^{73} -3.91744 q^{77} +(6.52601 - 11.3034i) q^{79} -4.43429 q^{83} +(-11.9210 - 20.6478i) q^{85} +(3.47016 + 6.01050i) q^{89} +(-4.35192 - 7.53775i) q^{91} +(-10.1705 + 13.7165i) q^{95} +(2.58704 - 4.48089i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 4 q^{5} + 4 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 4 q^{5} + 4 q^{7} - 8 q^{11} + 4 q^{17} - 8 q^{19} - 8 q^{23} - 4 q^{25} + 4 q^{31} + 16 q^{37} + 4 q^{41} + 6 q^{43} - 4 q^{47} - 16 q^{49} + 16 q^{53} + 16 q^{55} - 12 q^{59} - 8 q^{61} + 48 q^{65} - 2 q^{67} + 4 q^{71} - 4 q^{73} - 8 q^{77} + 22 q^{79} - 8 q^{83} - 8 q^{85} - 12 q^{89} + 2 q^{91} - 32 q^{95} + 24 q^{97}+O(q^{100}) \) 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
\(5\) 1.95872 3.39260i 0.875966 1.51722i 0.0202354 0.999795i \(-0.493558\pi\)
0.855730 0.517422i \(-0.173108\pi\)
\(6\) 0 0
\(7\) −2.04306 −0.772204 −0.386102 0.922456i \(-0.626179\pi\)
−0.386102 + 0.922456i \(0.626179\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 1.91744 0.578129 0.289065 0.957310i \(-0.406656\pi\)
0.289065 + 0.957310i \(0.406656\pi\)
\(12\) 0 0
\(13\) 2.13010 + 3.68945i 0.590784 + 1.02327i 0.994127 + 0.108219i \(0.0345148\pi\)
−0.403343 + 0.915049i \(0.632152\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 3.04306 5.27073i 0.738050 1.27834i −0.215322 0.976543i \(-0.569080\pi\)
0.953372 0.301797i \(-0.0975865\pi\)
\(18\) 0 0
\(19\) −4.33039 0.497680i −0.993461 0.114176i
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −3.42711 5.93592i −0.714601 1.23773i −0.963113 0.269096i \(-0.913275\pi\)
0.248512 0.968629i \(-0.420058\pi\)
\(24\) 0 0
\(25\) −5.17316 8.96018i −1.03463 1.79204i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 1.34277 + 2.32574i 0.249345 + 0.431879i 0.963344 0.268268i \(-0.0864512\pi\)
−0.713999 + 0.700147i \(0.753118\pi\)
\(30\) 0 0
\(31\) 1.46839 0.263730 0.131865 0.991268i \(-0.457903\pi\)
0.131865 + 0.991268i \(0.457903\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −4.00178 + 6.93128i −0.676424 + 1.17160i
\(36\) 0 0
\(37\) 3.93677 0.647202 0.323601 0.946194i \(-0.395107\pi\)
0.323601 + 0.946194i \(0.395107\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 1.70029 2.94499i 0.265541 0.459930i −0.702164 0.712015i \(-0.747783\pi\)
0.967705 + 0.252085i \(0.0811161\pi\)
\(42\) 0 0
\(43\) 3.77725 6.54239i 0.576026 0.997705i −0.419904 0.907569i \(-0.637936\pi\)
0.995929 0.0901369i \(-0.0287304\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 4.96050 + 8.59183i 0.723563 + 1.25325i 0.959563 + 0.281494i \(0.0908301\pi\)
−0.236000 + 0.971753i \(0.575837\pi\)
\(48\) 0 0
\(49\) −2.82591 −0.403702
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −4.91922 8.52033i −0.675706 1.17036i −0.976262 0.216593i \(-0.930505\pi\)
0.300556 0.953764i \(-0.402828\pi\)
\(54\) 0 0
\(55\) 3.75572 6.50510i 0.506422 0.877148i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −1.61595 + 2.79891i −0.210379 + 0.364387i −0.951833 0.306616i \(-0.900803\pi\)
0.741454 + 0.671004i \(0.234136\pi\)
\(60\) 0 0
\(61\) −4.70477 8.14891i −0.602385 1.04336i −0.992459 0.122577i \(-0.960884\pi\)
0.390074 0.920783i \(-0.372449\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 16.6891 2.07003
\(66\) 0 0
\(67\) 5.28173 + 9.14823i 0.645266 + 1.11763i 0.984240 + 0.176838i \(0.0565870\pi\)
−0.338973 + 0.940796i \(0.610080\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 2.21715 3.84021i 0.263127 0.455749i −0.703944 0.710255i \(-0.748580\pi\)
0.967071 + 0.254506i \(0.0819129\pi\)
\(72\) 0 0
\(73\) −6.33488 + 10.9723i −0.741441 + 1.28421i 0.210398 + 0.977616i \(0.432524\pi\)
−0.951839 + 0.306598i \(0.900809\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −3.91744 −0.446434
\(78\) 0 0
\(79\) 6.52601 11.3034i 0.734234 1.27173i −0.220825 0.975313i \(-0.570875\pi\)
0.955059 0.296417i \(-0.0957917\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −4.43429 −0.486727 −0.243363 0.969935i \(-0.578251\pi\)
−0.243363 + 0.969935i \(0.578251\pi\)
\(84\) 0 0
\(85\) −11.9210 20.6478i −1.29301 2.23956i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 3.47016 + 6.01050i 0.367837 + 0.637112i 0.989227 0.146389i \(-0.0467652\pi\)
−0.621390 + 0.783501i \(0.713432\pi\)
\(90\) 0 0
\(91\) −4.35192 7.53775i −0.456206 0.790171i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −10.1705 + 13.7165i −1.04347 + 1.40728i
\(96\) 0 0
\(97\) 2.58704 4.48089i 0.262675 0.454966i −0.704277 0.709925i \(-0.748729\pi\)
0.966952 + 0.254959i \(0.0820621\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −4.79182 8.29967i −0.476804 0.825848i 0.522843 0.852429i \(-0.324871\pi\)
−0.999647 + 0.0265808i \(0.991538\pi\)
\(102\) 0 0
\(103\) −17.7128 −1.74530 −0.872648 0.488351i \(-0.837599\pi\)
−0.872648 + 0.488351i \(0.837599\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −10.8578 −1.04966 −0.524830 0.851207i \(-0.675871\pi\)
−0.524830 + 0.851207i \(0.675871\pi\)
\(108\) 0 0
\(109\) 3.41296 5.91141i 0.326902 0.566211i −0.654994 0.755634i \(-0.727329\pi\)
0.981895 + 0.189424i \(0.0606620\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 6.16868 0.580300 0.290150 0.956981i \(-0.406295\pi\)
0.290150 + 0.956981i \(0.406295\pi\)
\(114\) 0 0
\(115\) −26.8510 −2.50386
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −6.21715 + 10.7684i −0.569925 + 0.987139i
\(120\) 0 0
\(121\) −7.32343 −0.665766
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −20.9439 −1.87328
\(126\) 0 0
\(127\) −10.4095 18.0299i −0.923698 1.59989i −0.793642 0.608385i \(-0.791818\pi\)
−0.130056 0.991507i \(-0.541516\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −1.61773 + 2.80199i −0.141342 + 0.244811i −0.928002 0.372575i \(-0.878475\pi\)
0.786660 + 0.617386i \(0.211808\pi\)
\(132\) 0 0
\(133\) 8.84725 + 1.01679i 0.767154 + 0.0881669i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 0.405993 + 0.703200i 0.0346863 + 0.0600785i 0.882847 0.469660i \(-0.155623\pi\)
−0.848161 + 0.529738i \(0.822290\pi\)
\(138\) 0 0
\(139\) −1.77725 3.07829i −0.150745 0.261097i 0.780757 0.624835i \(-0.214834\pi\)
−0.931501 + 0.363738i \(0.881500\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 4.08434 + 7.07428i 0.341550 + 0.591581i
\(144\) 0 0
\(145\) 10.5204 0.873672
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −10.3445 + 17.9173i −0.847458 + 1.46784i 0.0360112 + 0.999351i \(0.488535\pi\)
−0.883469 + 0.468489i \(0.844799\pi\)
\(150\) 0 0
\(151\) 17.0408 1.38676 0.693381 0.720571i \(-0.256120\pi\)
0.693381 + 0.720571i \(0.256120\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 2.87616 4.98165i 0.231019 0.400136i
\(156\) 0 0
\(157\) 9.62918 16.6782i 0.768492 1.33107i −0.169889 0.985463i \(-0.554341\pi\)
0.938381 0.345604i \(-0.112326\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 7.00178 + 12.1274i 0.551817 + 0.955776i
\(162\) 0 0
\(163\) 1.32801 0.104018 0.0520088 0.998647i \(-0.483438\pi\)
0.0520088 + 0.998647i \(0.483438\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −6.49033 11.2416i −0.502237 0.869900i −0.999997 0.00258498i \(-0.999177\pi\)
0.497760 0.867315i \(-0.334156\pi\)
\(168\) 0 0
\(169\) −2.57467 + 4.45946i −0.198052 + 0.343036i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −2.49211 + 4.31646i −0.189472 + 0.328174i −0.945074 0.326856i \(-0.894011\pi\)
0.755603 + 0.655030i \(0.227344\pi\)
\(174\) 0 0
\(175\) 10.5691 + 18.3062i 0.798947 + 1.38382i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 16.6101 1.24150 0.620748 0.784010i \(-0.286829\pi\)
0.620748 + 0.784010i \(0.286829\pi\)
\(180\) 0 0
\(181\) 3.52382 + 6.10343i 0.261923 + 0.453664i 0.966753 0.255712i \(-0.0823099\pi\)
−0.704830 + 0.709377i \(0.748977\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 7.71103 13.3559i 0.566926 0.981945i
\(186\) 0 0
\(187\) 5.83488 10.1063i 0.426688 0.739046i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 16.1687 1.16992 0.584962 0.811061i \(-0.301109\pi\)
0.584962 + 0.811061i \(0.301109\pi\)
\(192\) 0 0
\(193\) −8.32250 + 14.4150i −0.599067 + 1.03761i 0.393892 + 0.919157i \(0.371128\pi\)
−0.992959 + 0.118458i \(0.962205\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −9.23191 −0.657746 −0.328873 0.944374i \(-0.606669\pi\)
−0.328873 + 0.944374i \(0.606669\pi\)
\(198\) 0 0
\(199\) −6.82031 11.8131i −0.483479 0.837410i 0.516341 0.856383i \(-0.327294\pi\)
−0.999820 + 0.0189729i \(0.993960\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −2.74335 4.75162i −0.192545 0.333499i
\(204\) 0 0
\(205\) −6.66079 11.5368i −0.465210 0.805767i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −8.30326 0.954271i −0.574349 0.0660083i
\(210\) 0 0
\(211\) −2.10068 + 3.63849i −0.144617 + 0.250484i −0.929230 0.369502i \(-0.879528\pi\)
0.784613 + 0.619986i \(0.212862\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −14.7972 25.6294i −1.00916 1.74791i
\(216\) 0 0
\(217\) −3.00000 −0.203653
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 25.9281 1.74411
\(222\) 0 0
\(223\) −7.82927 + 13.5607i −0.524287 + 0.908092i 0.475313 + 0.879817i \(0.342335\pi\)
−0.999600 + 0.0282750i \(0.990999\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 28.1758 1.87009 0.935046 0.354525i \(-0.115358\pi\)
0.935046 + 0.354525i \(0.115358\pi\)
\(228\) 0 0
\(229\) 7.23731 0.478255 0.239128 0.970988i \(-0.423139\pi\)
0.239128 + 0.970988i \(0.423139\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −8.96405 + 15.5262i −0.587255 + 1.01715i 0.407336 + 0.913279i \(0.366458\pi\)
−0.994590 + 0.103876i \(0.966875\pi\)
\(234\) 0 0
\(235\) 38.8649 2.53527
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 2.08256 0.134710 0.0673549 0.997729i \(-0.478544\pi\)
0.0673549 + 0.997729i \(0.478544\pi\)
\(240\) 0 0
\(241\) 5.90955 + 10.2356i 0.380667 + 0.659335i 0.991158 0.132688i \(-0.0423609\pi\)
−0.610490 + 0.792024i \(0.709028\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −5.53517 + 9.58719i −0.353629 + 0.612503i
\(246\) 0 0
\(247\) −7.38802 17.0369i −0.470088 1.08403i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 0.434292 + 0.752216i 0.0274123 + 0.0474795i 0.879406 0.476072i \(-0.157940\pi\)
−0.851994 + 0.523552i \(0.824607\pi\)
\(252\) 0 0
\(253\) −6.57126 11.3818i −0.413132 0.715565i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −5.85243 10.1367i −0.365065 0.632311i 0.623722 0.781646i \(-0.285620\pi\)
−0.988787 + 0.149336i \(0.952287\pi\)
\(258\) 0 0
\(259\) −8.04306 −0.499771
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 15.7038 27.1999i 0.968341 1.67722i 0.267982 0.963424i \(-0.413643\pi\)
0.700358 0.713791i \(-0.253024\pi\)
\(264\) 0 0
\(265\) −38.5414 −2.36758
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 7.68731 13.3148i 0.468704 0.811818i −0.530657 0.847587i \(-0.678055\pi\)
0.999360 + 0.0357685i \(0.0113879\pi\)
\(270\) 0 0
\(271\) −9.94574 + 17.2265i −0.604161 + 1.04644i 0.388023 + 0.921650i \(0.373158\pi\)
−0.992184 + 0.124787i \(0.960175\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −9.91922 17.1806i −0.598151 1.03603i
\(276\) 0 0
\(277\) 4.19698 0.252172 0.126086 0.992019i \(-0.459758\pi\)
0.126086 + 0.992019i \(0.459758\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 7.95872 + 13.7849i 0.474777 + 0.822339i 0.999583 0.0288837i \(-0.00919524\pi\)
−0.524805 + 0.851222i \(0.675862\pi\)
\(282\) 0 0
\(283\) −3.76269 + 6.51716i −0.223668 + 0.387405i −0.955919 0.293630i \(-0.905137\pi\)
0.732251 + 0.681035i \(0.238470\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −3.47380 + 6.01679i −0.205052 + 0.355160i
\(288\) 0 0
\(289\) −10.0204 17.3559i −0.589436 1.02093i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 21.7962 1.27335 0.636674 0.771133i \(-0.280310\pi\)
0.636674 + 0.771133i \(0.280310\pi\)
\(294\) 0 0
\(295\) 6.33039 + 10.9646i 0.368570 + 0.638382i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 14.6002 25.2882i 0.844350 1.46246i
\(300\) 0 0
\(301\) −7.71715 + 13.3665i −0.444809 + 0.770432i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −36.8613 −2.11067
\(306\) 0 0
\(307\) 15.3394 26.5685i 0.875463 1.51635i 0.0191951 0.999816i \(-0.493890\pi\)
0.856268 0.516531i \(-0.172777\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0.0530439 0.00300784 0.00150392 0.999999i \(-0.499521\pi\)
0.00150392 + 0.999999i \(0.499521\pi\)
\(312\) 0 0
\(313\) 4.07374 + 7.05593i 0.230262 + 0.398825i 0.957885 0.287152i \(-0.0927085\pi\)
−0.727623 + 0.685977i \(0.759375\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −13.1126 22.7118i −0.736479 1.27562i −0.954071 0.299580i \(-0.903154\pi\)
0.217592 0.976040i \(-0.430180\pi\)
\(318\) 0 0
\(319\) 2.57467 + 4.45946i 0.144154 + 0.249682i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −15.8008 + 21.3099i −0.879179 + 1.18571i
\(324\) 0 0
\(325\) 22.0387 38.1722i 1.22249 2.11741i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −10.1346 17.5536i −0.558738 0.967762i
\(330\) 0 0
\(331\) −0.359379 −0.0197533 −0.00987664 0.999951i \(-0.503144\pi\)
−0.00987664 + 0.999951i \(0.503144\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 41.3817 2.26093
\(336\) 0 0
\(337\) −14.3454 + 24.8470i −0.781443 + 1.35350i 0.149657 + 0.988738i \(0.452183\pi\)
−0.931101 + 0.364762i \(0.881150\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 2.81554 0.152470
\(342\) 0 0
\(343\) 20.0749 1.08394
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 7.64781 13.2464i 0.410556 0.711103i −0.584395 0.811469i \(-0.698668\pi\)
0.994951 + 0.100366i \(0.0320014\pi\)
\(348\) 0 0
\(349\) −5.75772 −0.308204 −0.154102 0.988055i \(-0.549248\pi\)
−0.154102 + 0.988055i \(0.549248\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 13.8950 0.739558 0.369779 0.929120i \(-0.379433\pi\)
0.369779 + 0.929120i \(0.379433\pi\)
\(354\) 0 0
\(355\) −8.68553 15.0438i −0.460980 0.798441i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −0.936774 + 1.62254i −0.0494410 + 0.0856344i −0.889687 0.456571i \(-0.849077\pi\)
0.840246 + 0.542206i \(0.182411\pi\)
\(360\) 0 0
\(361\) 18.5046 + 4.31030i 0.973928 + 0.226858i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 24.8165 + 42.9834i 1.29895 + 2.24985i
\(366\) 0 0
\(367\) −0.526011 0.911078i −0.0274576 0.0475579i 0.851970 0.523590i \(-0.175408\pi\)
−0.879428 + 0.476033i \(0.842074\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 10.0502 + 17.4075i 0.521783 + 0.903754i
\(372\) 0 0
\(373\) 33.6908 1.74444 0.872221 0.489111i \(-0.162679\pi\)
0.872221 + 0.489111i \(0.162679\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −5.72046 + 9.90813i −0.294619 + 0.510295i
\(378\) 0 0
\(379\) −35.1157 −1.80377 −0.901887 0.431972i \(-0.857818\pi\)
−0.901887 + 0.431972i \(0.857818\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −7.75054 + 13.4243i −0.396034 + 0.685951i −0.993233 0.116142i \(-0.962947\pi\)
0.597199 + 0.802093i \(0.296280\pi\)
\(384\) 0 0
\(385\) −7.67316 + 13.2903i −0.391060 + 0.677337i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 6.28215 + 10.8810i 0.318518 + 0.551689i 0.980179 0.198114i \(-0.0634817\pi\)
−0.661661 + 0.749803i \(0.730148\pi\)
\(390\) 0 0
\(391\) −41.7155 −2.10965
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −25.5652 44.2803i −1.28633 2.22798i
\(396\) 0 0
\(397\) 3.01924 5.22948i 0.151531 0.262460i −0.780259 0.625456i \(-0.784913\pi\)
0.931791 + 0.362996i \(0.118246\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −10.1557 + 17.5902i −0.507151 + 0.878412i 0.492814 + 0.870134i \(0.335968\pi\)
−0.999966 + 0.00827741i \(0.997365\pi\)
\(402\) 0 0
\(403\) 3.12781 + 5.41753i 0.155808 + 0.269867i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 7.54852 0.374166
\(408\) 0 0
\(409\) 17.0580 + 29.5453i 0.843462 + 1.46092i 0.886950 + 0.461865i \(0.152820\pi\)
−0.0434881 + 0.999054i \(0.513847\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 3.30149 5.71834i 0.162455 0.281381i
\(414\) 0 0
\(415\) −8.68553 + 15.0438i −0.426356 + 0.738470i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 0.326693 0.0159600 0.00797999 0.999968i \(-0.497460\pi\)
0.00797999 + 0.999968i \(0.497460\pi\)
\(420\) 0 0
\(421\) −10.0195 + 17.3543i −0.488320 + 0.845795i −0.999910 0.0134352i \(-0.995723\pi\)
0.511590 + 0.859230i \(0.329057\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −62.9689 −3.05444
\(426\) 0 0
\(427\) 9.61213 + 16.6487i 0.465163 + 0.805687i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −17.2297 29.8427i −0.829924 1.43747i −0.898097 0.439797i \(-0.855051\pi\)
0.0681736 0.997673i \(-0.478283\pi\)
\(432\) 0 0
\(433\) −6.10993 10.5827i −0.293625 0.508573i 0.681039 0.732247i \(-0.261528\pi\)
−0.974664 + 0.223674i \(0.928195\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 11.8865 + 27.4105i 0.568610 + 1.31122i
\(438\) 0 0
\(439\) −5.93356 + 10.2772i −0.283193 + 0.490505i −0.972169 0.234279i \(-0.924727\pi\)
0.688976 + 0.724784i \(0.258060\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −0.154752 0.268039i −0.00735250 0.0127349i 0.862326 0.506354i \(-0.169007\pi\)
−0.869678 + 0.493619i \(0.835674\pi\)
\(444\) 0 0
\(445\) 27.1883 1.28885
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −22.5275 −1.06314 −0.531570 0.847015i \(-0.678398\pi\)
−0.531570 + 0.847015i \(0.678398\pi\)
\(450\) 0 0
\(451\) 3.26020 5.64684i 0.153517 0.265899i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −34.0968 −1.59848
\(456\) 0 0
\(457\) 29.6679 1.38781 0.693903 0.720069i \(-0.255890\pi\)
0.693903 + 0.720069i \(0.255890\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 11.2530 19.4908i 0.524105 0.907777i −0.475501 0.879715i \(-0.657733\pi\)
0.999606 0.0280618i \(-0.00893351\pi\)
\(462\) 0 0
\(463\) 30.7041 1.42694 0.713471 0.700685i \(-0.247122\pi\)
0.713471 + 0.700685i \(0.247122\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 38.0932 1.76274 0.881372 0.472423i \(-0.156620\pi\)
0.881372 + 0.472423i \(0.156620\pi\)
\(468\) 0 0
\(469\) −10.7909 18.6904i −0.498277 0.863041i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 7.24265 12.5446i 0.333017 0.576803i
\(474\) 0 0
\(475\) 17.9425 + 41.3757i 0.823259 + 1.89845i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 12.4755 + 21.6082i 0.570020 + 0.987304i 0.996563 + 0.0828364i \(0.0263979\pi\)
−0.426543 + 0.904467i \(0.640269\pi\)
\(480\) 0 0
\(481\) 8.38573 + 14.5245i 0.382356 + 0.662261i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −10.1346 17.5536i −0.460188 0.797069i
\(486\) 0 0
\(487\) 16.6747 0.755603 0.377802 0.925887i \(-0.376680\pi\)
0.377802 + 0.925887i \(0.376680\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −12.6881 + 21.9764i −0.572604 + 0.991780i 0.423693 + 0.905806i \(0.360734\pi\)
−0.996297 + 0.0859741i \(0.972600\pi\)
\(492\) 0 0
\(493\) 16.3445 0.736118
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −4.52976 + 7.84577i −0.203187 + 0.351931i
\(498\) 0 0
\(499\) 5.92421 10.2610i 0.265204 0.459347i −0.702413 0.711770i \(-0.747894\pi\)
0.967617 + 0.252423i \(0.0812274\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 11.0125 + 19.0742i 0.491024 + 0.850478i 0.999947 0.0103338i \(-0.00328942\pi\)
−0.508923 + 0.860812i \(0.669956\pi\)
\(504\) 0 0
\(505\) −37.5433 −1.67065
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 8.16512 + 14.1424i 0.361913 + 0.626851i 0.988276 0.152680i \(-0.0487905\pi\)
−0.626363 + 0.779532i \(0.715457\pi\)
\(510\) 0 0
\(511\) 12.9425 22.4171i 0.572543 0.991674i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −34.6944 + 60.0925i −1.52882 + 2.64799i
\(516\) 0 0
\(517\) 9.51145 + 16.4743i 0.418313 + 0.724539i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 35.3180 1.54731 0.773655 0.633607i \(-0.218426\pi\)
0.773655 + 0.633607i \(0.218426\pi\)
\(522\) 0 0
\(523\) 6.22971 + 10.7902i 0.272406 + 0.471821i 0.969477 0.245180i \(-0.0788472\pi\)
−0.697071 + 0.717002i \(0.745514\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 4.46839 7.73947i 0.194646 0.337137i
\(528\) 0 0
\(529\) −11.9901 + 20.7675i −0.521309 + 0.902934i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 14.4872 0.627510
\(534\) 0 0
\(535\) −21.2673 + 36.8361i −0.919466 + 1.59256i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −5.41851 −0.233392
\(540\) 0 0
\(541\) 11.6629 + 20.2007i 0.501427 + 0.868496i 0.999999 + 0.00164801i \(0.000524577\pi\)
−0.498572 + 0.866848i \(0.666142\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −13.3700 23.1576i −0.572710 0.991962i
\(546\) 0 0
\(547\) 2.26581 + 3.92449i 0.0968789 + 0.167799i 0.910391 0.413749i \(-0.135781\pi\)
−0.813512 + 0.581548i \(0.802447\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −4.65723 10.7396i −0.198405 0.457524i
\(552\) 0 0
\(553\) −13.3330 + 23.0935i −0.566978 + 0.982034i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −6.05782 10.4924i −0.256678 0.444579i 0.708672 0.705538i \(-0.249295\pi\)
−0.965350 + 0.260959i \(0.915961\pi\)
\(558\) 0 0
\(559\) 32.1837 1.36123
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 14.3553 0.605003 0.302502 0.953149i \(-0.402178\pi\)
0.302502 + 0.953149i \(0.402178\pi\)
\(564\) 0 0
\(565\) 12.0827 20.9279i 0.508323 0.880442i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −5.69927 −0.238926 −0.119463 0.992839i \(-0.538117\pi\)
−0.119463 + 0.992839i \(0.538117\pi\)
\(570\) 0 0
\(571\) −3.20155 −0.133981 −0.0669904 0.997754i \(-0.521340\pi\)
−0.0669904 + 0.997754i \(0.521340\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −35.4579 + 61.4150i −1.47870 + 2.56118i
\(576\) 0 0
\(577\) 18.4957 0.769985 0.384992 0.922920i \(-0.374204\pi\)
0.384992 + 0.922920i \(0.374204\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 9.05952 0.375852
\(582\) 0 0
\(583\) −9.43229 16.3372i −0.390646 0.676618i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 10.7487 18.6173i 0.443646 0.768417i −0.554311 0.832310i \(-0.687018\pi\)
0.997957 + 0.0638928i \(0.0203516\pi\)
\(588\) 0 0
\(589\) −6.35869 0.730787i −0.262005 0.0301116i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 23.2225 + 40.2225i 0.953633 + 1.65174i 0.737466 + 0.675384i \(0.236022\pi\)
0.216167 + 0.976356i \(0.430644\pi\)
\(594\) 0 0
\(595\) 24.3553 + 42.1846i 0.998469 + 1.72940i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 1.23013 + 2.13064i 0.0502617 + 0.0870557i 0.890062 0.455840i \(-0.150661\pi\)
−0.839800 + 0.542896i \(0.817328\pi\)
\(600\) 0 0
\(601\) −43.4329 −1.77167 −0.885833 0.464004i \(-0.846412\pi\)
−0.885833 + 0.464004i \(0.846412\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −14.3445 + 24.8455i −0.583189 + 1.01011i
\(606\) 0 0
\(607\) 14.2875 0.579911 0.289956 0.957040i \(-0.406359\pi\)
0.289956 + 0.957040i \(0.406359\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −21.1327 + 36.6030i −0.854939 + 1.48080i
\(612\) 0 0
\(613\) −5.03526 + 8.72133i −0.203372 + 0.352251i −0.949613 0.313425i \(-0.898524\pi\)
0.746241 + 0.665676i \(0.231857\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −2.72579 4.72121i −0.109736 0.190069i 0.805927 0.592015i \(-0.201667\pi\)
−0.915663 + 0.401946i \(0.868334\pi\)
\(618\) 0 0
\(619\) −1.48602 −0.0597282 −0.0298641 0.999554i \(-0.509507\pi\)
−0.0298641 + 0.999554i \(0.509507\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −7.08975 12.2798i −0.284045 0.491980i
\(624\) 0 0
\(625\) −15.1574 + 26.2534i −0.606295 + 1.05013i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 11.9798 20.7497i 0.477667 0.827344i
\(630\) 0 0
\(631\) 8.28173 + 14.3444i 0.329691 + 0.571041i 0.982450 0.186524i \(-0.0597222\pi\)
−0.652760 + 0.757565i \(0.726389\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −81.5575 −3.23651
\(636\) 0 0
\(637\) −6.01948 10.4260i −0.238501 0.413095i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 0.598395 1.03645i 0.0236352 0.0409373i −0.853966 0.520329i \(-0.825809\pi\)
0.877601 + 0.479392i \(0.159143\pi\)
\(642\) 0 0
\(643\) −5.91067 + 10.2376i −0.233094 + 0.403731i −0.958717 0.284362i \(-0.908218\pi\)
0.725623 + 0.688092i \(0.241552\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 40.6540 1.59827 0.799136 0.601150i \(-0.205291\pi\)
0.799136 + 0.601150i \(0.205291\pi\)
\(648\) 0 0
\(649\) −3.09849 + 5.36674i −0.121626 + 0.210663i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −18.4522 −0.722091 −0.361046 0.932548i \(-0.617580\pi\)
−0.361046 + 0.932548i \(0.617580\pi\)
\(654\) 0 0
\(655\) 6.33736 + 10.9766i 0.247621 + 0.428892i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 13.9429 + 24.1499i 0.543140 + 0.940746i 0.998721 + 0.0505517i \(0.0160980\pi\)
−0.455582 + 0.890194i \(0.650569\pi\)
\(660\) 0 0
\(661\) 7.33736 + 12.7087i 0.285390 + 0.494310i 0.972704 0.232051i \(-0.0745435\pi\)
−0.687314 + 0.726361i \(0.741210\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 20.7788 28.0236i 0.805769 1.08671i
\(666\) 0 0
\(667\) 9.20361 15.9411i 0.356365 0.617242i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −9.02111 15.6250i −0.348256 0.603197i
\(672\) 0 0
\(673\) −15.5272 −0.598531 −0.299265 0.954170i \(-0.596742\pi\)
−0.299265 + 0.954170i \(0.596742\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −10.9734 −0.421742 −0.210871 0.977514i \(-0.567630\pi\)
−0.210871 + 0.977514i \(0.567630\pi\)
\(678\) 0 0
\(679\) −5.28548 + 9.15472i −0.202838 + 0.351326i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 34.5032 1.32023 0.660115 0.751165i \(-0.270508\pi\)
0.660115 + 0.751165i \(0.270508\pi\)
\(684\) 0 0
\(685\) 3.18090 0.121536
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 20.9569 36.2984i 0.798393 1.38286i
\(690\) 0 0
\(691\) −32.2359 −1.22631 −0.613157 0.789961i \(-0.710101\pi\)
−0.613157 + 0.789961i \(0.710101\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −13.9245 −0.528188
\(696\) 0 0
\(697\) −10.3482 17.9236i −0.391965 0.678903i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 14.4261 24.9867i 0.544866 0.943735i −0.453750 0.891129i \(-0.649914\pi\)
0.998615 0.0526059i \(-0.0167527\pi\)
\(702\) 0 0
\(703\) −17.0478 1.95925i −0.642969 0.0738947i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 9.78996 + 16.9567i 0.368189 + 0.637723i
\(708\) 0 0
\(709\) 15.5486 + 26.9310i 0.583940 + 1.01141i 0.995007 + 0.0998090i \(0.0318232\pi\)
−0.411066 + 0.911606i \(0.634843\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −5.03232 8.71623i −0.188462 0.326425i
\(714\) 0 0
\(715\) 32.0003 1.19674
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 7.78108 13.4772i 0.290185 0.502615i −0.683668 0.729793i \(-0.739616\pi\)
0.973853 + 0.227178i \(0.0729498\pi\)
\(720\) 0 0
\(721\) 36.1883 1.34772
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 13.8927 24.0629i 0.515962 0.893672i
\(726\) 0 0
\(727\) −1.05762 + 1.83186i −0.0392251 + 0.0679399i −0.884971 0.465645i \(-0.845822\pi\)
0.845746 + 0.533585i \(0.179156\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −22.9888 39.8178i −0.850271 1.47271i
\(732\) 0 0
\(733\) −36.5909 −1.35152 −0.675759 0.737123i \(-0.736184\pi\)
−0.675759 + 0.737123i \(0.736184\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 10.1274 + 17.5412i 0.373047 + 0.646137i
\(738\) 0 0
\(739\) −6.62533 + 11.4754i −0.243717 + 0.422130i −0.961770 0.273858i \(-0.911700\pi\)
0.718053 + 0.695988i \(0.245033\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −8.63427 + 14.9550i −0.316761 + 0.548645i −0.979810 0.199930i \(-0.935928\pi\)
0.663050 + 0.748575i \(0.269262\pi\)
\(744\) 0 0
\(745\) 40.5241 + 70.1898i 1.48469 + 2.57156i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 22.1831 0.810551
\(750\) 0 0
\(751\) 3.32703 + 5.76259i 0.121405 + 0.210280i 0.920322 0.391162i \(-0.127927\pi\)
−0.798917 + 0.601441i \(0.794593\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 33.3782 57.8127i 1.21476 2.10402i
\(756\) 0 0
\(757\) 22.7980 39.4873i 0.828607 1.43519i −0.0705234 0.997510i \(-0.522467\pi\)
0.899131 0.437680i \(-0.144200\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 4.47448 0.162200 0.0810998 0.996706i \(-0.474157\pi\)
0.0810998 + 0.996706i \(0.474157\pi\)
\(762\) 0 0
\(763\) −6.97287 + 12.0774i −0.252435 + 0.437230i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −13.7686 −0.497155
\(768\) 0 0
\(769\) 0.310132 + 0.537164i 0.0111836 + 0.0193706i 0.871563 0.490283i \(-0.163107\pi\)
−0.860379 + 0.509654i \(0.829773\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −15.0219 26.0186i −0.540299 0.935825i −0.998887 0.0471762i \(-0.984978\pi\)
0.458588 0.888649i \(-0.348356\pi\)
\(774\) 0 0
\(775\) −7.59620 13.1570i −0.272864 0.472614i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −8.82860 + 11.9068i −0.316317 + 0.426604i
\(780\) 0 0
\(781\) 4.25124 7.36336i 0.152121 0.263482i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −37.7217 65.3359i −1.34635 2.33194i
\(786\) 0 0
\(787\) −41.7810 −1.48933 −0.744666 0.667437i \(-0.767391\pi\)
−0.744666 + 0.667437i \(0.767391\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −12.6030 −0.448110
\(792\) 0 0
\(793\) 20.0433 34.7160i 0.711758 1.23280i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 24.9231 0.882823 0.441411 0.897305i \(-0.354478\pi\)
0.441411 + 0.897305i \(0.354478\pi\)
\(798\) 0 0
\(799\) 60.3803 2.13610
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −12.1467 + 21.0388i −0.428649 + 0.742442i
\(804\) 0 0
\(805\) 54.8581 1.93349
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 20.5993 0.724232 0.362116 0.932133i \(-0.382055\pi\)
0.362116 + 0.932133i \(0.382055\pi\)
\(810\) 0 0
\(811\) 14.2831 + 24.7390i 0.501547 + 0.868705i 0.999998 + 0.00178759i \(0.000569009\pi\)
−0.498451 + 0.866918i \(0.666098\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 2.60119 4.50540i 0.0911158 0.157817i
\(816\) 0 0
\(817\) −19.6130 + 26.4513i −0.686172 + 0.925413i
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −5.18475 8.98026i −0.180949 0.313413i 0.761255 0.648453i \(-0.224584\pi\)
−0.942204 + 0.335040i \(0.891250\pi\)
\(822\) 0 0
\(823\) −17.9457 31.0829i −0.625549 1.08348i −0.988434 0.151649i \(-0.951542\pi\)
0.362885 0.931834i \(-0.381792\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 22.5782 + 39.1066i 0.785122 + 1.35987i 0.928926 + 0.370265i \(0.120733\pi\)
−0.143804 + 0.989606i \(0.545934\pi\)
\(828\) 0 0
\(829\) 30.6047 1.06294 0.531472 0.847076i \(-0.321639\pi\)
0.531472 + 0.847076i \(0.321639\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −8.59942 + 14.8946i −0.297952 + 0.516068i
\(834\) 0 0
\(835\) −50.8510 −1.75977
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 10.0089 17.3359i 0.345545 0.598502i −0.639907 0.768452i \(-0.721027\pi\)
0.985453 + 0.169950i \(0.0543607\pi\)
\(840\) 0 0
\(841\) 10.8940 18.8689i 0.375654 0.650651i
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 10.0861 + 17.4697i 0.346973 + 0.600975i
\(846\) 0 0
\(847\) 14.9622 0.514107
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −13.4917 23.3684i −0.462491 0.801058i
\(852\) 0 0
\(853\) 4.71715 8.17034i 0.161512 0.279747i −0.773899 0.633309i \(-0.781696\pi\)
0.935411 + 0.353562i \(0.115030\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 0.330247 0.572005i 0.0112810 0.0195393i −0.860330 0.509738i \(-0.829742\pi\)
0.871611 + 0.490199i \(0.163076\pi\)
\(858\) 0 0
\(859\) 5.34992 + 9.26634i 0.182537 + 0.316163i 0.942744 0.333518i \(-0.108236\pi\)
−0.760207 + 0.649681i \(0.774902\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 52.3471 1.78192 0.890958 0.454086i \(-0.150034\pi\)
0.890958 + 0.454086i \(0.150034\pi\)
\(864\) 0 0
\(865\) 9.76269 + 16.9095i 0.331941 + 0.574939i
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 12.5132 21.6735i 0.424482 0.735224i
\(870\) 0 0
\(871\) −22.5013 + 38.9733i −0.762426 + 1.32056i
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 42.7896 1.44655
\(876\) 0 0
\(877\) 27.5362 47.6942i 0.929833 1.61052i 0.146234 0.989250i \(-0.453285\pi\)
0.783598 0.621268i \(-0.213382\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 59.0183 1.98838 0.994188 0.107660i \(-0.0343357\pi\)
0.994188 + 0.107660i \(0.0343357\pi\)
\(882\) 0 0
\(883\) −14.8835 25.7790i −0.500871 0.867534i −0.999999 0.00100591i \(-0.999680\pi\)
0.499129 0.866528i \(-0.333654\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 3.74074 + 6.47915i 0.125602 + 0.217549i 0.921968 0.387266i \(-0.126581\pi\)
−0.796366 + 0.604815i \(0.793247\pi\)
\(888\) 0 0
\(889\) 21.2673 + 36.8361i 0.713283 + 1.23544i
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −17.2049 39.6748i −0.575741 1.32767i
\(894\) 0 0
\(895\) 32.5345 56.3514i 1.08751 1.88362i
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 1.97170 + 3.41509i 0.0657599 + 0.113899i
\(900\) 0 0
\(901\) −59.8778 −1.99482
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 27.6087 0.917743
\(906\) 0 0
\(907\) 18.0071 31.1892i 0.597916 1.03562i −0.395212 0.918590i \(-0.629329\pi\)
0.993128 0.117031i \(-0.0373378\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −41.2605 −1.36702 −0.683511 0.729941i \(-0.739548\pi\)
−0.683511 + 0.729941i \(0.739548\pi\)
\(912\) 0 0
\(913\) −8.50248 −0.281391
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 3.30512 5.72463i 0.109145 0.189044i
\(918\) 0 0
\(919\) −57.0889 −1.88319 −0.941595 0.336747i \(-0.890673\pi\)
−0.941595 + 0.336747i \(0.890673\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 18.8910 0.621805
\(924\) 0 0
\(925\) −20.3656 35.2742i −0.669616 1.15981i
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −7.19418 + 12.4607i −0.236033 + 0.408822i −0.959572 0.281462i \(-0.909181\pi\)
0.723539 + 0.690283i \(0.242514\pi\)
\(930\) 0 0
\(931\) 12.2373 + 1.40640i 0.401062 + 0.0460929i
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −22.8578 39.5908i −0.747529 1.29476i
\(936\) 0 0
\(937\) 1.78836 + 3.09753i 0.0584231 + 0.101192i 0.893758 0.448550i \(-0.148059\pi\)
−0.835335 + 0.549742i \(0.814726\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 5.70842 + 9.88728i 0.186089 + 0.322316i 0.943943 0.330108i \(-0.107085\pi\)
−0.757854 + 0.652424i \(0.773752\pi\)
\(942\) 0 0
\(943\) −23.3083 −0.759023
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 14.7671 25.5773i 0.479865 0.831151i −0.519868 0.854247i \(-0.674019\pi\)
0.999733 + 0.0230954i \(0.00735216\pi\)
\(948\) 0 0
\(949\) −53.9757 −1.75213
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −14.7483 + 25.5448i −0.477744 + 0.827477i −0.999675 0.0255109i \(-0.991879\pi\)
0.521930 + 0.852988i \(0.325212\pi\)
\(954\) 0 0
\(955\) 31.6699 54.8539i 1.02481 1.77503i
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −0.829467 1.43668i −0.0267849 0.0463928i
\(960\) 0 0
\(961\) −28.8438 −0.930446
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 32.6029 + 56.4699i 1.04952 + 1.81783i
\(966\) 0 0
\(967\) −18.0446 + 31.2541i −0.580274 + 1.00506i 0.415172 + 0.909743i \(0.363721\pi\)
−0.995447 + 0.0953215i \(0.969612\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −3.68637 + 6.38497i −0.118301 + 0.204904i −0.919095 0.394037i \(-0.871078\pi\)
0.800793 + 0.598941i \(0.204411\pi\)
\(972\) 0 0
\(973\) 3.63103 + 6.28913i 0.116405 + 0.201620i
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 33.9705 1.08681 0.543406 0.839470i \(-0.317134\pi\)
0.543406 + 0.839470i \(0.317134\pi\)
\(978\) 0 0
\(979\) 6.65383 + 11.5248i 0.212657 + 0.368333i
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −22.0857 + 38.2535i −0.704423 + 1.22010i 0.262476 + 0.964938i \(0.415461\pi\)
−0.966899 + 0.255158i \(0.917873\pi\)
\(984\) 0 0
\(985\) −18.0827 + 31.3202i −0.576163 + 0.997944i
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −51.7802 −1.64651
\(990\) 0 0
\(991\) 7.70048 13.3376i 0.244614 0.423684i −0.717409 0.696652i \(-0.754672\pi\)
0.962023 + 0.272968i \(0.0880054\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −53.4363 −1.69404
\(996\) 0 0
\(997\) −27.3218 47.3228i −0.865291 1.49873i −0.866758 0.498728i \(-0.833800\pi\)
0.00146761 0.999999i \(-0.499533\pi\)
\(998\) 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.bc.1873.4 8
3.2 odd 2 2736.2.s.ba.1873.1 8
4.3 odd 2 1368.2.s.m.505.4 yes 8
12.11 even 2 1368.2.s.l.505.1 8
19.7 even 3 inner 2736.2.s.bc.577.4 8
57.26 odd 6 2736.2.s.ba.577.1 8
76.7 odd 6 1368.2.s.m.577.4 yes 8
228.83 even 6 1368.2.s.l.577.1 yes 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1368.2.s.l.505.1 8 12.11 even 2
1368.2.s.l.577.1 yes 8 228.83 even 6
1368.2.s.m.505.4 yes 8 4.3 odd 2
1368.2.s.m.577.4 yes 8 76.7 odd 6
2736.2.s.ba.577.1 8 57.26 odd 6
2736.2.s.ba.1873.1 8 3.2 odd 2
2736.2.s.bc.577.4 8 19.7 even 3 inner
2736.2.s.bc.1873.4 8 1.1 even 1 trivial